Someone help me with this SAT math problem!?

Question

okay. so. graham walked to school at an average speed of 3 miles an hour, and jogged back along the same route at 5 miles an hour. if his total traveling time was 1 hour, what was the total number of miles in the round trip?

(the book tells me the answer is 3.75 miles, but i don't know how to get to that answer!)

Answer 1

It's a distance, rate, time thing. Set up d=r*t for each leg of the journey, then equate the distances (since it's the same) and solve for your unknown.

d1 = r1 * t1
d1 = distance to school
r1 = 3m/h walking speed to school
t1 = ??

d2 = r2 * t2
d2 = distance from school to home
r2 = 5m/h jogging speed back home
t2 = ???

They do tell us that t1 + t2 is 1 hr. So we have a third equation t1 + t2 = 1

Plug the first two equations into this third equation.

d1/r1 = t1 and d2/r2 = t2 therefore

d1/r1 + d2/r2 = 1 We can simplify further by knowing that d1=d2=d since the path to and from is the same.

d/r1 + d/r2 = 1 Now solve for d. First factor it out

d (1/r1 + 1/r2) = 1 divide by (1/r1 + 1/r2)

d = 1/(1/r1 + 1/r2) plug and chug

d = 1/(1/3 + 1/5)
d = 1/(5/15 + 3/15)
d = 1/(8/15)
d = 15/8 miles

total distance is 2d so the totals distance is 30/8 miles, which equals 3.75 miles.

Answer 2

time walked + time jogged = 1 hour
time walked = 1 hour - time jogged

distance walked = distance jogged

time walked * rate of walking = time jogged * rate of jogging

(1 - time jogged) * 3 = time jogged * 5

3 - 3* time jogged = 5* time jogged

3 = 8* time jogged
3/8 = time jogged

distance jogged = time jogged * rate of jogging
distance jogged = (3/8) 5 = 15/8 miles

however, the question asks for round trip, so multiply by 2

2* (15/8) = 30/8 = 3 6/8 = 3.75 miles

Answer 3

The distance each way is x miles
It took him x/3 hrs to get there and x/5 hrs to get back
x/3 + x/5 = 1 hr
5x + 3x = 15
8x = 15
x = 15/8 (one-way distance)
2x = 15/4 = 3.75 (two-way distance)