David's horse

Consider the formula $distance = rate \times time$

Let $x$ be the amount of time taken riding and $4 - x$ walking.

$10x + 3(4 - x) = 29.5$

$x= 2.5 hours$ which is equal to $150 minutes.$

Setting up the equation we find that $10*t_{h}+3*t_{w}=29.5$ and $t_{w}+t_{h}=4$ . Solving we find that $7*t_{h}=17.5$ . Solving for $t_{h}$ and multiplying by $60$ we find that the answer is $150$ .

Let's say David was riding his horse for $x$ hours.

Then, he was walking for $4 - x$ hours, as the total trip was of $4$ hours.

Since the total distance travelled is $29.5 = \frac{59}{2}$ miles, we have

$10 . x + 3 . (4 - x) = \frac{59}{2}$

$10x + 12 - 3x = \frac{59}{2}$

$7x + 12 = \frac{59}{2}$

$7x = \frac{59}{2} - 12$

$7x = \frac{35}{2}$

$x = \frac{35}{2 \times 7}$

$x = \frac{5}{2}$ hours

In minutes, it will be

$x = \frac{5}{2} \times 60$ minutes

$x = 150$ minutes

That's the answer!

THIS IS QUITE SIMPLE!

The total distance travelled is 29.5 miles. We know that when David is riding he is at 10 miles/hour and when he is walking he is at 3 miles/hour.

Let 'R' be riding time taken, 'W' be walking time taken and 'T' be the total time taken; hence we can write;

T= R + W

which is; 29.5T= 10R + 3W ( since riding speed is 10mph and walking speed is 3mph)------> eq. 1

We also know that the total amount of time taken is 4 hours; hence;

4=R + W ------> eq.2

From eq.2 we get; W= 4 - R------->eq.3

Putting eq.3 in eq.1; We get; 29.5T= 10R + 3(4-R)

29.5T= 10R + 12 - 3R

29.5T= 7R + 12

R=29.5T-12 / 7

R=2.5T

Therefore David rode for 2.5 hours = 150 minutes! ENJOY!

29.5 = 25 + 4.5 ---> 25/10 hour + 4.5 /3 hour = 4 hour ---> 2 .5 hour + 1. 5 hour = 4 hour. ---> [2 .5 hour] + 1. 5 hour = 4 hour. ----> So, David was riding 2.5 hour = 2 .5 x 60 minutes = 150 minutes. Answer : 150

Let $x$ be the distance he made by riding his horse.Let $x_1$ be the distance he made by walking.Let $t$ be the time he was riding his horse.Let $t_1$ be the time he was walking during the trip.We have :

$10=\frac{x}{t}$ $(1)$

$3=\frac{x_1}{t_1}$ $(2)$

From the first equation we have :

$10t_1-10.5=x_1$

$3t_1=x_1$

Therefore we have $10t_1-10.5=3t_1$ where we obtain $t_1=1.5$ hours and $t=2.5$ hours which is equal to $150$ minutes .So $\boxed{t=150 }$

The answer is 150 and arrived by simple arithmetic.

David travels for 4 hours. In this time, he travels 29.5 miles.

D=st, you can do this for both horse and walking, finding the sum at the end- which is equal to the total distance (29.5mi).

Thus if h is time on horse,

29.5mi=10h + 3w, w=4-h 29.5mi=10h+3(4-h) 29.5=7h+12, h=17.5/7 h=2.5

The question asks you to convert this into minutes - 2.5 hours = 150 minutes.

The key leap here was realising that time walking can be written as (4-h). This means you have only one unknown in your equation for time on horse and thus that it can be solved to give 150 minutes.

the only combination for 29.5 mil is 29.5 = 10+10+5+3+1.5 i.e he rode the horse for the first 2 and a half hrs and then walked for the rest. so he rode for 150 mins.

time on horse= x, time on foot = y, x+y=4 or x= 4-y 10x+3y=29.5 substituting x. 40-10y+3y=29.5 or y = 1.5 and x=2.5 so 2.5*60=150min

Let the time travelled by David while riding be x hours and while walking be y hours.

       RIDING

SPEED=10 miles/hr
TIME =x hr
SINCE D=S*T,
D=10x

      WALKING

SPEED=3 miles/hr TIME =Y hr
SINCE D=S*T,
D=3y

ACCORDING TO QUESTION, 10x+3y =29.5 and x+ y =4

By solving, x=2.5 hr and y=1.5 hr

Therefore time spent by David riding horse=2.5 hr =(2.5 *60) min =150 minutes

x/3 + (29.5 - x)/(10) = 4

x/3 - x/10 = 1.05

7x/30 = 1.05

x = 4.5 miles

So therefore David spend (29.5 - 4.5)/10 * 60 = 150 minutes riding the horse.

let x hour David ride and y hour David walk then 10x+3y=29.5..........(i) but y=4-x..........(ii) then x=2.5 in minutes x=2.5*60 x=150

David rides his horse 2.5 hrs and travels 25 miles.(2 hr=20 miles and for 30 min=5 miles) by walking for 1.5 hrs,he covers 4.5 miles(1 hr=3 miles and for 30 min=1.5 miles) so for total 4 hrs trip he travels 25+4.5=29.5 miles . hence David rides his horse for 2.5 hrs i.e.., 150 min

x= time spent to travel with horse y = time spent when walking

29.5 = 10 x + 3 y x + y = 4

then,

y = 4 - x 29.5 = 10 x + 3 (4 - x) = 10 x + 3 4 - 3*x

17.5 = 7*x

x = 2.5 in minutes = 2.5*60 = 150 minutes

You can set up this equation:

10x + 3(4 - x) = 29.5

where x is the number of hours he rides the horse. The quantity (4 - x) represents the rest of the 4-hour trip, when he was walking. From this we obtain x=2.5, but since x is in hours, we must multiply by 60 to get the number of minutes he rode his horse.

The final answer is 150 minutes.

Here's the variable and what they represents in my explanation Time spent on: Walking = a Riding on horse = b

The time spent = 4 hours. 4 hours = a hours + b hours Because the total time spent on the journey is the total time spent riding on horse(b) and walking(a). But let's erase the 'hours' so... 4 = a + b

For the other equation: 29.5(miles) = 10b + 3a The total distance traveled by David is of course the sum of the distance of him walking and riding on horse. Why 10b? It comes from 10 mi/hour * b hour = 10b miles. So is 3a.

The rest left is combining the two equations by using either subtitution or elimination method. In the end, the result is 2.5 hours for b which is 150 minutes.

Yo,by rights,let x=riding on a horse,y=walking,total miles=29.5 miles, total hour=4 hours,

x + y = 4 10y + 3x = 29.5

by substituting,

y = 4 - x into 10x + 3y = 29.5 ,you will get x=2.5 hours(riding on horse),by multiply 60 to 2.5 hours you will get 150 mins,as 1hour=60 mins,thanks....

let x be the time(in hrs) spent for travelling by horse and y by walk. According to the problem, x + y = 4 and 10x+3y=29.5 . On solving these equations, x=2.5hrs i.e., 150 minutes