Question

lenidiagal6. Two cars are traveling in the same direction, one at 50 mph, one at 55 mph.If the slower car started an hour earlier, how many hours will it take thefaster car to catch up to it?a. 11 b. 9 c. 10 d. 5.5

Answer 1

It is said that the speed of the first car is 50mph and the speed of another car is 55mph.

Let t be the time at which the second car catches the first car.

It is known that speed is distance over time, so distance is the product of speed and time as follows:

`\begin{gathered} \text{speed}=\frac{\text{ Distance}}{\text{ Time}} \\ \text{ Distance=speed}*\text{ Time} \end{gathered}`

Both cars will cover the same distance but the time for second car will be t-1 since it started an hour late, so it follows:

`\begin{gathered} 50t=55(t-1) \\ 50t=55t-55 \\ 55=5t \\ t=11 \end{gathered}`

So in 11 hours, the second car will catch up to the first car. Both the cars would have travelled 550 miles by then. But the second car will be travelling for only 10 hours, so the answer is 10

Option C is correct.