SOLUTION: Help!
At the Indianapolis 500, Carter and Daniels were participants. Daniels'motor blew after 240 miles, and Carter was out after 270 miles. If Carter's average rate was 20mph mor
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At the Indianapolis 500, Carter and Daniels were participants. Daniels'motor blew after 240 miles, and Carter was out after 270 miles. If Carter's average rate was 20mph mor
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Question 167469: Help!
At the Indianapolis 500, Carter and Daniels were participants. Daniels'motor blew after 240 miles, and Carter was out after 270 miles. If Carter's average rate was 20mph more than Daniels, and their total time was 3 hours, how fast was each averaging?
Thank you for your help, whichever kind person answers my question!
Lauren Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! At the Indianapolis 500, Carter and Daniels were participants. Daniel's motor
blew after 240 miles, and Carter was out after 270 miles. If Carter's average
rate was 20mph more than Daniels, and their total time was 3 hours,
how fast was each averaging?
;
Let s = D's speed
then
(s+20) = C's speed
:
Write a time equation: Time = dist/speed
:
D's time + C's time = 5 hrs + = 3
:
Multiply equation by s(s+20)
s(s+20)* + s(s+20)* = s(s+20)*3
;
Cancel out the denominators and you have:
240(s+20) + 270s = 3s(s+20)
:
240s + 4800 + 270s = 3s^2 + 60s
:
510s + 4800 = 3s^2 + 60s
;
0 = 3s^2 + 60s - 510s - 4800
:
A quadratic equation
3s^2 - 450s - 4800 = 0
:
Simplify divide by 3
s^2 - 150s - 1600 = 0
:
Factors to:
(s - 160)(x + 10) = 0
:
Positive solution is what we want here:
s = +160 mph is D's speed
then
160 + 20 = 180 mph is C's speed.
:
:
Check solution in original time equation + =
1.5 + 1.5 = 3 hrs; confirms our solution
:
by a kind person!
