Question 99387
Lee can ride his bicycle 50 mi in the same time it takes him to drive 125 mi. If his driving rate is 30 mi/h faster than his rate bicycling, find each rate
:
Recognize the fact that the bicycle trip time = the car trip time
:
Let s = speed of the bicycle
Then
(s+30) = speed of the car
:
Write a time equation: Time = dist/speed
 Bike time = Car time
{{{50/s}}} = {{{125/((s+30))}}}
:
Cross multiply
125s = 50(s+30)
125s = 50s + 1500
125s - 50s = 1500
75s = 1500
s = 1500/75
s = 20 mph is speed of the bicycle
:
20 + 30 = 50 mph is car's speed
:
:
Check solution by finding the time:
50/20 = 2.5 hrs
125/50 = 2.5 hrs, also
: