Question

Julie recently drove to visit her parents who live 240 miles away. On her way there her average speed was 11 miles per hour faster than on her way home (she ran into some bad weather). If Julie spent a total of 8 hours driving, find the two rates.

Answer 1

Answer: The two rates are 55 and 66 miles per hour.

Explanation:

Let the average speed of julie on her way home be x.

It is given that on her way there her average speed was 11 miles per hour faster than on her way home (she ran into some bad weather).

So the average speed on her way there is x + 11.

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

It is given that Julie's parents live 240 miles away.

Time taken by Julie on on her way there is,

$t_1=\frac{240}{x+11}$

Time taken by Julie on on her way home is,

$t_2=\frac{240}{x}$

Since the total time take by julie is 8 hours.

$t_1+t_2=8$

$\frac{240}{x+11}+\frac{240}{x}=8$

$240(\frac{1}{x+11}+\frac{1}{x})=8$

$\frac{30(x+x+11)}{x(x+11)}=1$

$30(2x+11)=x^2+11x$

$x^2-49x-330=0$

$x^2-55x+6x-330=0$

$(x+6)(x-55)=0$

Equate each factor equal to 0. The speed in always positive, therefore average speed of julie on her way home is 55 miles per hour and average speed of julie on her way there is 66 miles per hour.