Question

On a drive from one city to​ another, the person averaged 51 mph. If he had been able to average 72 ​mph, he would have reached his destination 7 hrs earlier. What is the driving distance between one city and the​ other?

Answer 1

Answer: 1224 miles

Step-by-step explanation:

Given

the average speed of a person is 51 mph

If speed is increased to 72 mph, he would have reached 7 hr earlier

Suppose d and t be the distance and time taken

$\Rightarrow t_1=\dfrac{d}{51}$

If the speed is 72 mph

$\Rightarrow t_2=\dfrac{d}{72}$

Also, $t_1-t_2=7$

$\Rightarrow \dfrac{d}{51}-\dfrac{d}{72}=7\\\\\Rightarrow \dfrac{1}{51}-\dfrac{1}{72}=\dfrac{7}{d}\\\\\Rightarrow \dfrac{24-17}{1224}=\dfrac{7}{d}\\\\\Rightarrow \dfrac{7}{1224}=\dfrac{7}{d}\\\\\Rightarrow d=1224\ miles$