Question

Two cars are driving east on the same highway. One car is currently at mile marker 36 driving 1.1 miles per minute. The second car is behind at mile marker 30 driving 1.25 miles per minute. In how many minutes will they both be at the same mile marker on the highway?​

Answer 1

40 minutes

Explanation:

Let the mile marker where both cars cross at the same time be X

Car 1 will travel a distance of X-36 at 1.1miles/minute.
Therefore time taken for Car 1 to reach mile marker X is (X-36)/1.1 ...(1)

Car 2 will have to travel a distance of X-30 miles at 1.25 miles/minute.
Time taken for Car 2 to reach mile marker X = (X-30)/1.25 ...(2)

These times have to be equal

So (X-36)/1.1 = (X-30)/1.25

Cross multiplying,

1.25(X-36) = 1.1(X-30) ==> 1.25X - 45 = 1.1X - 33

Rearranging we get

1.25X - 1.1X = 45 - 33

0.15X = 12

X = 80 . This is the mile marker at which both cars are even

Time taken t can be found by substituting for X in any of the equations (1) or (2).

Using (2) we get

(80-30)/1.25 = 50/1.25 = 40 minutes


Cross Check
In 40 minutes, Car 1 travels 40 x 1.1 = 44 miles and the mile marker it will reach is 36 + 44 = 80
Car 2 travels 1.25 x 40 = 50 miles and the mile marker it will reach in this time is 30 + 50 = 80