What is the Velocity?

Algebra Level 2

John was driving his car to the city A to visit his family. He was in constant velocity and see 3 transit signs informing the distance left to arrive in city A.

He saw one sign informing:

"City A a 0 b ㎞ \boxed{ a0b ㎞} left"

After 45 minutes he saw other sign:

"City A b a ㎞ \boxed{ ba ㎞} left"

After 45 minutes he saw more other sign:

"City A a b ㎞ \boxed{ ab ㎞} left"

What was the speed that John was driving?

Note: a0b , ba and ab are 3 and 2 digit numbers. The a0b have the 0 on middle.

50km/h 60 km/h 40 km/h 45 km/h

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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1 solution

Sandeep Chouhan
Jun 8, 2014

Time taken in both intervals(from a0b to ba and from ba to ab) are same=45min If speed is constant, then distance travelled in both intervals is same. From there we get 6a=b. Now possible values of a0b could be between 101-109 as half of it is 2 digit number.. So 106 is only number satisfying two conditions. Hence a=1 and b=6 Hence got distances now find speed.

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used my instinct..........lol

ashutosh mahapatra - 6 years, 11 months ago

How to know 6a = b ? can u explain further ?

Bleach Byakuya - 6 years, 11 months ago

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You have equals distance from a0b to ba and ba to ab , or:

a 0 b − b a = b a − a b a0b-ba=ba-ab these numbers are decimals:

35 is 10x3+1x5 AB is 10xB+1xB in other words:

100 a + b − 10 b − a = 10 b + a − 10 a − b 100a+b-10b-a=10b+a-10a-b

Simplifyng you get 6 a = b 6a=b

Have only one solution 6*1=6 a=1 b=6

Look:

106-61=45 61-16=45

To find the velocity you make:

45km in 45min or 1km in 1min

60km in 60min --- 60km/h

Thus the is the velocity 60 k m / h 60km/h

Victor Paes Plinio - 6 years, 11 months ago

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