SOLUTION: A biker completed a trip from town A to town B. If he rode 3 km per hour faster, then he could spend one hour less for this trip. If he rode 2 km per hour slower, he would be one h

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Question 239415: A biker completed a trip from town A to town B. If he rode 3 km per hour faster, then he could spend one hour less for this trip. If he rode 2 km per hour slower, he would be one hour late.
Find the distance between towns, speed of the biker, and time of traveling.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A biker completed a trip from town A to town B.
If he rode 3 km per hour faster, then he could spend one hour less for this trip.
If he rode 2 km per hour slower, he would be one hour late.
Find the distance between towns, speed of the biker, and time of traveling.
:
Let s = the biker's speed
then
(s+3) = 3 km faster speed
and
(s-2) = 2 km slower speed
:
Let d = dist from a to b
:
Write two time equations: time = dist/speed
- = 1 (he went 3 km/h faster)
and
- = 1 (he went 2 km/hr slower)
:
Both equations = 1, so we can write it:
- = -
simplify, divide each term by d
- = -
combine like terms
+ - =
:
- =
:
Multiply by s(s+3)(s-2) to get rid of the denominators:
2(s+3)(s-2) - s(s-2) = s(s+3)
:
2(s^2 + s - 6) - s^2 + 2s = s^2 + 3s
:
2s^2 + 2s - 12 - s^2 + 2s = s^2 + 3s
Combine like terms on the left
2s^2 - s^2 - s^2 + 2s + 2s - 3s - 12 = 0
:
s - 12 = 0
s = 12 km/hr is the speed
:
Find the dist between towns using
- = 1
:
- = 1
Multiply by 60
5d - 4d = 60
d = 60 km is the distance
:
Find the time: = 5 hrs, time of travel
:
:
Check solutions in:
- = 1
:
- =
6 - 5 = 1 hr