SOLUTION: Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours. Which equatio

Question 1122162: Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours.
Which equation can be used to find the time it took Stu to hike the trail?

Found 2 solutions by Theo, josgarithmetic:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours. Which equation can be used to find the time it took Stu to hike the trail?

going he traveled at an average of 3 miles per hour.
coming back he traveled at an average of 5 miles per hour.
he traveled for a total of 3 hours.
since you already know the total time it took, you are probably looking for the time it took him to go out and the time it took him to come back.

the general formula to use for these types of problems is R * T = D
R is the rate of travel.
T is the time of travel.
D is the distance traveled.

going, the formula would become 3 * T = D
coming back the formula would become 5 * (5 - T) = D

D is same in both formulas since she traveled the same distance going as coming back.

since she traveled a total of 3 hours, then T is the time going and 3 - T is the time coming back.

you have 2 equations that need to be solved simultaneously.

they are:

3 * T = D
5 * (3 - T) = D

simplify these equations to get:

3T = D
15 - 5T = D

since D = 3T in the first equation, replace D with 3T in the second equation to get:

15 - 5T = 3T

add 5T to both sides of this equation to get 15 = 8T

solve for T to get T = 15/8 = 1.875.

it took her 1.875 hours to go out on the trial.
it took her 3 - 1.875 = 1.125 hours to come back.

to confirm this is accurate, replace T with 1.875 and 3 - T with 1.125 in both original equationws and solve for D.

you will get:

3 * T = D becomes 3 * 1.875 = D which results in D = 5.625 miles.
5 * (3 - T) = D becomes 5 * 1.125 = D which results in D = 5.625 miles.

the distance is the same, so the times must be right.

the general formula that i normally use to solve these types of problems is rate * time = distance.

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE HIKE 3 d/3 d RAN 5 d/5 d TOTAL 3

This information allows for finding the one-way distance, d.
, from which the time each way can be found.

SPEED TIME DISTANCE HIKE 3 h 3h=d RAN 5 3-h 5(3-h)=d TOTAL 3

This information as arranged allows to find the hiking time, h.
Note, "HIKE" and "RAN" are the same distance.

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