It's vacation time
Marvin drives from his hometown to the hometown of Kylene. After 2 hours of driving he noticed that he covered 100 kilometers. He calculated that if he continued driving at the same speed, he would end up been 15 minutes late. So he increased his speed by 25 km/hr and arrived at Kylene's hometown 5 minutes earlier. How far is Marvin's hometown to Kylene's hometown in kilometers?
The answer is 150.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
2 solutions
The initial speed of Marvin is
V = t d = 2 h r s 1 0 0 k m = 5 0 h r k m
we let Y be the remaining distance
if he uses the the same speed, he would end up 15 minutes late
y = V ( t + 6 0 1 5 ) = 5 0 t + 1 2 . 5
he increased his speed by 2 5 k p h , he arrived 5 minutes earlier
y = V ( t − 6 0 5 ) = 7 5 t − 6 . 2 5
y = y
5 0 t + 1 2 . 5 = 7 5 t − 6 . 2 5
t = 4 3 h r s
y = 5 0 t + 1 2 . 5 = 5 0 k m
This problem is good, except it's confusing to discuss "5 minutes earlier". I think perhaps you mean "5 minutes early"? Also, it says "late" and "early" without specifying in the problem there is some exact time Marvin is aiming for; this is implied but still confusing to read. It also is good practice to specify in words how you're equating the two representations as opposed to just saying y = y.
Log in to reply
I agree about the wording. "5 minutes earlier" sounds almost like they would still be 10 minutes late, with the context of the previous sentence. It would make more sense to just say "5 minutes early."
Initial speed = 100 km / 2 hr = 50 km/hr
Remaining distance = d and time to travel it = t then d = 50*t (eqn 1)
If speed is increased by 25 time will be reduced by 20 minutes or 1/3 hour ( 15 - (-5) = 20)
New situation is d = 75 * (t - 1/3) (eqn 2)
Setting equations equal and solving for t results in t = 1
Plugging into eqn 1 we get d = 50
Therefore 100 + 50 = 150 km