SOLUTION: A bicyclist was going from point A to point B with a speed of 12 km/h. On the way back he increased his speed to 18 km/h and covered the distance in 15 minutes less. What is the di

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A bicyclist was going from point A to point B with a speed of 12 km/h. On the way back he increased his speed to 18 km/h and covered the distance in 15 minutes less. What is the di      Log On


   

Question 1107629: A bicyclist was going from point A to point B with a speed of 12 km/h. On the way back he increased his speed to 18 km/h and covered the distance in 15 minutes less. What is the distance between point A and point B?
Found 2 solutions by josgarithmetic, JThomson:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Fifteen minutes is the same as one-fourth of an hour.
                   SPEED       TIME       DISTANCE
AtoB               12          d/12         d
BtoA               18          d/18         d
DIFFERENCE                    1%2F4


Question asks for d, and it is found in solving d%2F12-d%2F18=1%2F4.

Answer by JThomson(12) About Me  (Show Source):
You can put this solution on YOUR website!

Let the distance covered by the cyclist in
kilometres be 'd' and time 't'.

Distance = Speed × Time

Distance travelled at a constant speed of 12km/h from A to B is;

d = 12t

Distance travelled on cyclist's return journey is;

d = 18(t-0.25)

* Note that the cyclist increased his speed to 18km/h and therefore covered the same distance 15 minutes less.

15 minutes in hours is 15/60 = 1/4 or 0.25

12t = 18(t-0.25)

12t= 18t-4.5

6t = 4.5

t = 0.75 or 3/4 hours

Distance between points A and B therefore is;

12×0.75 = 9 km or 18×(0.75-0.25) = 18×0.5 = 9km