[Math help] Fred has 5 hours at his disposal. How far (in miles) can he ride his bicycle, going at 10 miles...

per hour, and returning by the same route at 4 miles per hour?

a) 9 3/5
b) 10 1/2
c) 12 3/4
d) 14 2/7
e) 15 1/7

Suppose that Fred takes x hours traveling to a spot a certain distance away and takes 5 - x hours to return (note that x + (5 - x) = 5, so the total trip is 5 hours). Since Fred travels at a rate of 10 miles per hour there, we see that the distance he travels there is:
d = rt = 10x.

Then, since he travels at a rate of 4 miles per hour back, the distance he travels back is:
d = rt = 4(5 - x).

Since these two distances are the same, we have the equation:
10x = 4(5 - x).

This solves to yield x = 10/7.

Therefore, Fred can travel 10x = 100/7 = 14 2/7 miles.

I hope this helps!

first determine the ratio of going out vs return. assume he goes for 1 hr= 10 miles. the return =10/4=2.5hr so going +return =3.5>> 5 / 3.5=1.42857=1 3/7 so he can ride out 1+3/7 hrs and the return trip will take 3+4/7 hrs the going out will cover 14.2857 miles and the return will cover the same. The whole trip will take 5 hours. Just in time to watch Howdy Doody on TV.

Let the distance be x miles

Time taken = x /10 + x / 4 = 5


MULTIPLY BY 20

2x + 5x = 100

7x = 100

x = 100 /7 = 14.285714 miles

ANSWER 14 2/7 miles = It is d)
CHECK

14.29 /10 = 1.429 hours

14.29/4 = 3.571 hours

ADD = 5 hours

Let x = hours at 10 mph, let 5-x = hours at 4 mph.

10x = (5-x)4
10x = 20 - 4x
14x = 20.
x = 20/14 = 10/7

10*10/7 = 100/7 one way

round trip = 200/7; not one of the choices