SOLUTION: Members of the Healthy Reading Club ran from their club house to a first rest stop at a speed of 9 km/h, and from there to the second rest stop at a speed of 5 km/h. They returned
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Question 1149025: Members of the Healthy Reading Club ran from their club house to a first rest stop at a speed of 9 km/h, and from there to the second rest stop at a speed of 5 km/h. They returned along the same course, running at 10 km/h from the second rest stop to the first, and at 6 km/h the rest of the way to the club house. If it took a total of 2.5 hours to run both ways between the club house and the first rest stop, and 3 hours to run both ways between the first and second rest stops. How far, in km, did they run altogether? Answer by ikleyn(52813) (Show Source):
Let x be the distance from the house to the first stop.
For this distance, you have THIS "time" equation
+ = 2.5 hours.
Multiply both sides by 36 and find
4x + 6x = 90,
10x = 90
x = 90/10 = 9 miles.
Next, let y be the distance from the first stop to the second stop.
For this distance, you have THIS "time" equation
+ = 3 hours.
Multiply both sides by 10 and find
2y + y = 30,
3y = 30
y = 30/3 = 10 miles.
Then the total one way distance is 9 miles + 10 miles = 19 miles.
The two way distance is 2*19 = 38 miles.
Solved.
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Fresh formulation of traditional "time equation" problems.
My congratulations to the person who invented/created it (!)
