SOLUTION: A car travels 25km an hour faster than a bus for a journey of 500km. if the bus takes 10 hours more than the car, the speed of the car and the bus is

Question 924063: A car travels 25km an hour faster than a bus for a journey of 500km. if the bus takes 10 hours more than the car, the speed of the car and the bus is

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = speed of car
y = speed of bus
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x = y + 25
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s = d/t
t = d/s
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time of car:
a = 500/x
---
time of bus:
b = 500/x + 10
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speed of the car:
s = d/t
x = y + 25
d/a = d/b + 25
500/a = 500/b + 25
500/(500/x) = 500/(500/x + 10) + 25
x = 500/(500/x + 10) + 25
x - 25 = 500/(500/x + 10)
(x - 25)(500/x + 10) = 500
500 + 10x - 12500/x - 250 = 500
10x - 12500/x = 250
10xx - 12500 = 250x
10xx - 250x - 12500 = 0
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the above quadratic equation is in standard form, with a=10, b=-250, and c=-12500
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
10 -250 -12500
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 = 50
x = -25
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the negative root doesn't fit the problem statement, so use the positive root
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x = speed of car = 50 kph
y = speed of bus = 25 kph
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php

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