SOLUTION: On a recent trip, Sarah's car traveled 20 mph faster on the first 160 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's c

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Question 934632: On a recent trip, Sarah's car traveled 20 mph faster on the first 160 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the
first part of the trip
Found 2 solutions by TimothyLamb, lwsshak3:
Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website!
x = speed on first part
y = speed on second part
x = y + 20
y = x - 20
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s = d/t
t = d/s
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time on first part:
t = time on first part
t = 160/x
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time on second part:
4 - t = 80/y
4 - t = 80/(x - 20)
t = 4 - 80/(x - 20)
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equate times:
160/x = 4 - 80/(x - 20)
160/x + 80/(x - 20) = 4
160(x - 20)/x(x - 20) + 80x/x(x - 20) = 4
160(x - 20) + 80x = 4x(x - 20)
160x - 3200 + 80x = 4xx - 80x
4xx - 80x - 80x - 160x + 3200 = 0
4xx - 320x + 3200 = 0
xx - 80x + 800 = 0
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the above quadratic equation is in standard form, with a=1, b=-80 and c=800
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -80 800
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = 68.2842712
x = 11.7157288
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the root x=11.7 would make y negative, which doesn't fit the problem statement, so use the first root:
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answer:
x = speed on first part = 68.2842712 mph
y = speed on second part = 48.2842712 mph
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Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
On a recent trip, Sarah's car traveled 20 mph faster on the first 160 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip
***
let x=speed of sarah's car for first 160 miles
(x-20)=speed of sarah's car for remaining 80 miles
travel time=distance/speed

lcd:x(x-20)
160x-3200+80x=4x(x-20)
160x-3200+80x=4x^2-80x
4x^2-320x+3200=0
x^2-80x+800=0
solve for x by quadratic formula:

a=1, b=-80, c=800

x=11.72 (reject)
or
x=68.28
speed of sarah's car for first 160 miles=68.28 mph