Answer this word problem...

Question

Whitney left school and drove 7 miles to meet her mother at a restaurant. Her mother left at the same time and drove 8 miles, traveling 5 mi/h faster than her daughter. If the two arrived at the restaurant at the same time, what was Whitney’s speed?

 

a. 51 m/h
b. 35 mi/h
c. 46 mi/h
d. 30 mi/h

Answer 1

Assuming that both drivers are moving at a constant speed, we can use the formula

distance  = speed * time

Let x = Whitney's speed (in mph)

x + 5 = mom's speed (in mph)

 

t = the time that they both travel

 

Whitney travel's 7 miles, so using the distance formula:

xt = 7

t = 7/x

 

And for mom,

(x + 5)t = 8

t = 8/(x + 5)

 

Using the transitive property of equaltiy

t = 7/x

and

t = 8/(x + 5)

 

So,

7/x = 8/(x + 5)

Cross multiplying,

7x + 35 = 8x

x = 35 mph (Whitney's speed)