A car passes a landmark traveling at a constant rate of 45 km/h. 2 hours later, a second car passes the same landmark traveling in the same direction at 70 km/h. How much time after the second car passes the landmark will it overtake the first car?

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A car passes a landmark traveling at a constant rate of 45 km/h. 2 hours later, a second car passes the same landmark traveling in the same direction at 70 km/h. How much time after the second car passes the landmark will it overtake the first car?

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Answer 1 · 2017-02-06T13:09:14

$5 hours 36 minutes$ $5 " hours " 36 " minutes"$

Explanation:

The key to this problem is realising that at the point where the second car overtakes the first, they will BOTH be the SAME distance from the landmark.

$Distance = speed \times time$ $"Distance" = "speed" xx "time"$

We can write that distance in two different ways - one for each car.

Let the time for the first car to be overtaken be $t$ $t$

$D_{1} = 45 \times t$ $D_1 = 45 xx t$

The time for the second car to reach the the first is 2 hours less than the first car. Time = $t - 2$ $t-2$

$D_{2} = 70 \times (t - 2)$ $D_2 = 70 xx (t-2)$

But $D_{2} = D_{1}$ $D_2 = D_1$

$70 (t - 2) = 45 t$ $70(t-2) = 45t$

$70 t - 140 = 45 t$ $70t -140 = 45t$

$70 t - 45 t = 140$ $70t -45t = 140$

$25 t = 140$ $25t = 140$

$t = \frac{140}{25}$ $t = 140/25$

$t = 5.6 hours = 5 hours 36 minutes$ $t =5.6 "hours" = 5 " hours " 36 " minutes"$

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A car passes a landmark traveling at a constant rate of 45 km/h. 2 hours later, a second car passes the same landmark traveling in the same direction at 70 km/h. How much time after the second car passes the landmark will it overtake the first car?

1 Answer

Explanation:

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