SOLUTION: Hi, Can somebody please help me out? Our teacher instructed us to answer a few questions and I'm unfortunately stuck here on the third which is: A motorcycle driver travels 15

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, Can somebody please help me out? Our teacher instructed us to answer a few questions and I'm unfortunately stuck here on the third which is: A motorcycle driver travels 15       Log On


   

Question 881083: Hi,
Can somebody please help me out?
Our teacher instructed us to answer a few questions and I'm unfortunately stuck here on the third which is:
A motorcycle driver travels 15 kph faster than a bicycle rider. The motorcycle driver covers 60 km in two hours less than the time it takes the bicycle rider to travel the same distance.
I figured it would be something like
Speed
Let x = bicycle driver
x+15 = motorcycle rider
Time
Let x = motorcycle driver
x+2 = bicycle driver
60 = total
x+x+2=60
2x+2=60
2x+2-60
2x-58
x=29
x+x+15=60
2x+15=60
2x+15-60
2x-45
x=22.5
Any help would be appreciated! I'm still trying to solve this though.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
R%5Bm%5D=15%2BR%5Bb%5D
D=60
T%5Bm%5D=T%5Bb%5D-2
.
.
.
1.R%5Bm%5D%2AT%5Bm%5D=60
2.R%5Bb%5D%2AT%5Bb%5D=60
From eq. 1,
%2815%2BR%5Bb%5D%29%28T%5Bb%5D-2%29=60
From eq. 2,
R%5Bb%5D=60%2FT%5Bb%5D
Substituting,
%2815%2B60%2FT%5Bb%5D%29%28T%5Bb%5D-2%29=60
15T%5Bb%5D-30%2B60-120%2FT%5Bb%5D=60
15T%5Bb%5D-120%2FT%5Bb%5D=30
15T%5Bb%5D%5E2-120=30T%5Bb%5D
15T%5Bb%5D%5E2-30T%5Bb%5D-120=0
T%5Bb%5D%5E2-2T%5Bb%5D-8=0
%28T%5Bb%5D-4%29%28T%5Bb%5D%2B2%29=0
Only the positive solution make sense for time,
T%5Bb%5D-4=0
T%5Bb%5D=4
Then
R%5Bb%5D=60%2F4
R%5Bb%5D=15
and
R%5Bm%5D=15%2B15
R%5Bm%5D=30
and
T%5Bm%5D=4-2
T%5Bm%5D=2