Question

Two cars travel in the same direction along a
straight highway, one at a constant speed of
59 mi/h and the other at 79 mi/h.
Assuming they start at the same point, how
much sooner does the faster car arrive at a
destination 12 mi away?

Answer 1

Answer on Question #70178 Physics / Other

Two cars travel in the same direction along a straight highway, one at a constant speed of $v_{2} = 59 \, \mathrm{mi/h}$ and the other at $v_{1} = 79 \, \mathrm{mi/h}$. Assuming they start at the same point, how much sooner does the faster car arrive at a destination $l = 12 \, \mathrm{mi}$ away?

Solution:

The time of motion for faster car

$$t _ {1} = \frac {l}{v _ {1}} = \frac {1 2 \, \mathrm{mi}}{7 9 \, \mathrm{mi/h}} = \frac {1 2}{7 9} \, \mathrm{h}$$

The time of motion for slower car

$$t _ {2} = \frac {l}{v _ {2}} = \frac {1 2 \, \mathrm{mi}}{5 9 \, \mathrm{mi/h}} = \frac {1 2}{5 9} \, \mathrm{h}$$

So, the faster car arrive at a destination sooner on

$$\Delta t = t _ {2} - t _ {1} = \frac {1 2}{5 9} - \frac {1 2}{7 9} = 0.05 \, \mathrm{h} = 3 \, \mathrm{min}.$$

Answers: 3 min.

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