<PRE><B>Question 890173</B>
a car travels 20 kph faster than a truck.
 it covers 350 km in two hours less than the time it takes for the truck to travel the same distance.
 what is the speed of both vehicles?
:
Let s = the speed of the truck
then
(s+20) = the speed of the car
:
Write a time equation time = dist/speed
;
Truck time - car time = 2 hrs
{{{350/s}}} - {{{350/((s+20))}}} = 2
Multiply the equation b s(s+20), cancel the denominators, and you have
350(s+20) - 350s = 2s(s+20)
350s + 7000 - 350s = 2s^2 + 40s
Combine to form a quadratic equation
2s^2 + 40s - 7000 = 0
Simplify divide by 2
s^2 + 20s - 3500 = 0
Factors to 
(s+70)(s-50) = 0
the positive solution is what we want here
s = 50 km/h is the speed of the truck
then obviously;
70 km is the speed of the car
:
:
Confirm this by finding the travel time of each
350/50 = 7 hrs
350/70 = 5 hrs
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differ: 2 hrs
 
:
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