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Find the distance between the two towns ...?
A walker and a jogger left the town of Pi at the same time, heading toward the town of Epsilonville. The walker and jogger travel at constant speeds of 6 km/h and 10 km/h, respectively.
At the same time, a biker left Epsilonville, heading toward the town of Pi. The biker travels at a constant speed of 14 km/h.
If the biker passed the walker 4 minutes after passing the jogger, how far apart are the towns Pi and Epsilonville?
2 Answers
- daSVgrouchLv 77 years agoFavorite Answer
let x be the time at which the first meeting happened
then the distance between the cities, d = 10x + 14x
then, 4 minutes later the second meeting happens
6(x+4) + 14(x+4) = d
equating these expressions for d gives
24x = 20x+80
4x = 80
x = 20 minutes = 1/3 hour when the first meeting happened
substitute this into the first expression
the total distance is then (14+10) (1/3) = 8 km apart
MechEng used the wrong speed for the biker in the expression for the distance after 4 additional minutes passed
it should have been 14(x + 1/15) + 6(x + 1/15)
- MechEng2030Lv 77 years ago
Assume that the biker met the jogger after x hours.
14x + 10x = Total distance between the towns of Pi and Epsilonville.
Now from the problem, it becomes apparent that the biker meets the walker at time (x + 4/60) = (x + 1/15) hours.
So therefore:
14x + 10x = 14(x + 1/15) + 6(x + 1/15)
24x = 20x + 20/15
4x = 20/15
x = 1/3 hours
Therefore total distance between towns = 24(1/3 hours) = 8 km
