SOLUTION: Problem solving: Riding a bike. Cesar enjoys riding his bike from Washington, DC to Bethesda, Maryland and back a total of 30 miles on the Capital Crescent path. The trip to Bethe

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Problem solving: Riding a bike. Cesar enjoys riding his bike from Washington, DC to Bethesda, Maryland and back a total of 30 miles on the Capital Crescent path. The trip to Bethe      Log On


   

Question 526467: Problem solving:
Riding a bike. Cesar enjoys riding his bike from Washington, DC to Bethesda, Maryland and back a total of 30 miles on the Capital Crescent path. The trip to Bethesda is uphill most of the distance. The bike's average speed going to Bethesda is 5 mph slower than the average speed returning to DC. If the round trip takes 4.5 hours, find the average speed in each direction.
Please explain and show me the formula you plan to use to solve the problem.
Thanks
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Returning to DC speed = x mph
Going to Bethesda x-5 mph
Distance between them is 30 miles
Time going to bethseda + time returning to Dc = 4.5 hours
t=d/r
15/x + 15/(x-5)= 4.5 hours
LCD = x(x-5)
Multiply by LCD
15(x-5)+15x=4.5 * x(x-5)
15x-75+15x=4.5x^2-22.5x
4.5x^2-52.5x+75=0
multiply by 2
9x^2-105x+150=0
/3
3x^2-35x+50=0
Find the roots of the equation by quadratic formula

a= 3 , b= -35 , c= 50

b^2-4ac= 1225 + -600
b^2-4ac= 625 %09sqrt%28%09625%09%29=%0925%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 35 + 25 )/ 6
x1= 10.00
x2=( 35 -25 ) / 6
x2= 1.67

x=10
Speed returning = 10 mph
Speed while going is 5 mph
m.ananth@hotmail.ca