SOLUTION: A car traveled 510 miles in 8 hours. The car traveled the first 300 miles at a constant rate before increasing its speed by 10 mph. Then it traveled another 210 miles at the increa

Question 481446: A car traveled 510 miles in 8 hours. The car traveled the first 300 miles at a constant rate before increasing its speed by 10 mph. Then it traveled another 210 miles at the increased speed. Find the rate of the car for the first 300 miles
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A car traveled 510 miles in 8 hours.
The car traveled the first 300 miles at a constant rate before increasing its speed by 10 mph.
Then it traveled another 210 miles at the increased speed.
Find the rate of the car for the first 300 miles.
:
let s = the speed for the 1st 300 mi
then
(s+10) = speed for the remaining 210 mi
:
Write a time equation: time = dist/speed
+ = 8
:
multiply by s(s+10) and cancel the denominators, resulting in:
300(s+10) + 210s = 8s(s+10)
:
300s + 3000 + 210s = 8s^2 + 80s
510s + 3000 = 8s^2 + 80s
Combine like terms on the right
0 = 8s^2 + 80s - 510s - 3000
A quadratic equation
8s^2 - 430s - 3000 = 0
Find s using the quadratic formula; a=8, b=-430, c=-3000
the positive solution: 60 mph
:
:
Check by finding the total of the times
300/60 = 5 hrs
210/70 = 3 hrs
--------------
total: 8 hrs
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