math word problem

Question

Mr. Duncan traveled to a city 240 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 10 mph less than his speed going. If the total time for the round trip was 7 hours, at what rate of speed did he travel to the city? (Round your answer to the nearest tenth.)

Answer 1

Hi Russell,

 

If we let Mr. Duncan's speed be "v" on the way to the city,

then his speed on the way back was "v-10".

 

The time it took to get to the meeting would then be 240 miles / v (miles/hour) = (240/v) hours

The time it took to get back home would then be 240/(v-10) hours.

 

If the round trip was 7 hours, that means that the

trip to the meeting (240/v) + the trip home 240/(v-10) must be 7 hours.  

 

In math:

 

240/v + 240/(v-10) = 7

 

Written with "better fractions":

 

240       240

----  + -------  = 7

  v        v-10

 

We need to "get rid of" the denominators, so multiply both (WHOLE) sides by

"v" and "v-10".

 

v(v-10)240           240 v (v-10)

-------------    +   -----------------    =  7 v (v-10)

    v                           v-10

 

This simplifies to

 

240(v-10)    + 240 v  = 7v (v-10)

 

Distributing:

 

240v - 2400 +  240 v = 7 v² - 70 v

 

Combine like terms:

 

480 v - 2400  = 7 v² - 70 v

 

Move EVERYTHING to the right side, so that the left side is zero.

 

0 = 7v² -70v - 480v + 2400

 

Combine like terms:

 

0 = 7v² - 550v + 2400

 

The solutions (roots) of this equation are 4.637 mph, and 73.934 mph

 

Which is the most reasonable for the speed at which a car travels?

 

I believe that the answer is 73.9 miles per hour.

 

Working it again using 73.9 miles/hr, I find that it works out, so this was the correct choice.

 

Final answer is 73.9 miles per hour.