# Math Help - need help

1. ## need help

. You can determine the speed of a car by measuring the time it takes to travel between mile markers on a highway. (a) How many seconds should elapse between two consecutive mile markers if the car’s average speed is 65 mi/h? (b) What is the car’s average speed if it takes 65 s to travel between the mile markers?

2. Originally Posted by cruzangyal
. You can determine the speed of a car by measuring the time it takes to travel between mile markers on a highway. (a) How many seconds should elapse between two consecutive mile markers if the car’s average speed is 65 mi/h? (b) What is the car’s average speed if it takes 65 s to travel between the mile markers?
Note that 1 hour = 3600 seconds

The car is moving at the same speed, so it's speed is constant.

Now, $\mbox {Speed} = \frac { \mbox { Distance }}{ \mbox { Time }}$

The distance the car travels in 3600 seconds is 65 miles, how many seconds does it take to travel 1 mile moving at the same speed. Since the speeds must be equal, we can equate the formulas:

Let the amount of seconds the car takes to travel 1 mile be $x$.

$\frac { \mbox { Distance}_1 \mbox { }}{ \mbox { Time}_1 \mbox { }} = \frac { \mbox { Distance}_2 \mbox { }}{ \mbox { Time}_2 \mbox { }}$

$\Rightarrow \frac {65 \mbox { miles }}{ 3600 \mbox { seconds }} = \frac {1 \mbox { mile }}{x \mbox { seconds }}$ .........Now we solve for $x$

$\Rightarrow 65x = 3600$ .................................I cross-multiplied (I left out the units).

$\Rightarrow x = \frac {3600}{65} \approx 55.38 \mbox { seconds }$

Part (b) is similar