Question

The average speed of Car 1 = 45 mph.

The average speed of Car 2 = 65 mph.
Time elapsed between the start of Car 1 and start of Car 2 = 18 minutes.

How long before Car 2 overtakes Car 1? ____ hour.

Answer 1

Car2 overtakes Car1 after 0.675 hours

Explanation:

To solve this question, we must know that

Speed = distance / time

Speed_car1 = 45 mph = distance_car1/ time_1

Speed_car2= 65 mph = distance_car2/ time_2

We know that

time1 - time2 = 18 minutes = 0.3 h

And, at the time of the overtake, both cars will have traveled the same distance.

So,

distance_car1 = 45 mph * time1 = distance_car2 = 65 mph * time2

time1 / time2 = 65/45

time1 = 1.444*time2

Then,

1.444*time2- time2 = 0.3 h

time2 = 0.675 h

time1 = 0.975 h

Car2 overtakes Car1 after 0.675 hours

Answer 2

`\boxed{\text{0.675 h}}`

Explanation:

18 min = 0.3 h

Car 1 started 0.3 h before Car 2.

Let t = time of Car 2. Then

t + 0.3 = time of Car 1

Distance = speed × time, and both cars travel the same distance. Then

`\begin{array}{rcl}45(t + 0.3) & = & 65t\\45t + 13.5 & = & 65t\\20t & = & 13.5\\t & = & \textbf{0.675 h}\\\end{array}\\\text{Car will overtake Car 1 in } \boxed{\textbf{0.675 h}}`

Check:

`\begin{array}{rcl}45(0.675 + 0.3) & = & 65 * 0.675\\45 * 0.975 & = & 43.875\\43.875 & = & 43.875\\\end{array}`

OK.