word problem

Question

Mr. Jackson traveled to a city 390 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 8 mph less than his speed going. If the total time for the round trip was 14 hours, at what rate of speed did he travel to the city? (Round your answer to the nearest tenth.)

Answer 1

Hi again, Russell.

To answer this, just use the answer I gave a few minutes earlier to Mr. Duncan's road trip, but substitute "390" everywhere it says 240.  And substitute "v-8" everywhere it says v-10.  And substitute "14" for all of the "7 hours"And you can get the answer...  

 

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" "v-8".

The time it took to get to the meeting would then be 240 390 miles / v (miles/hour) = (240 390/v) hours
The time it took to get back home would then be 240 390/(v-10 8) hours.

If the round trip was 7 14 hours, that means that the
trip to the meeting (390/v) + the trip home 390/(v-8) must be 14 hours.

In math:

390/v + 390/(v-8) = 14

Written with "better fractions":

390         390
---- + ------- = 14
v             v-8

We need to "get rid of" the denominators, so multiply both (WHOLE) sides by
"v" and "v-8".

v(v-8)390            240 v (v-8)
------------- + ----------------- = 14 v (v-8)
    v                         v-8

This simplifies to

390(v-8) + 390 v = 14v (v-8)

Distributing:

390v - 3120 + 390 v = 14 v² - 112 v

Combine like terms:

780 v - 3120 = 14 v² - 112 v

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

0 = 14v² -112v - 780v + 3120

Combine like terms:

0 = 14v² - 892v + 3120

The solutions (roots) of this equation are 3.714 mph, and 60 mph.

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

I believe that the answer is 60 miles per hour.

Working it again using 60 miles/hr, I find that it works out, so this was the correct choice.

Final answer is 60 miles per hour.