Question 1190217: A car leaves a city 20 minutes after a truck leaves the same city. The truck is traveling at an average speed of 60kph and the car is traveling at an average speed of 80kph. How long will it take for the car to overtake the truck?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
A car leaves a city 20 minutes after a truck leaves the same city.
The truck is traveling at an average speed of 60kph and the car is traveling
at an average speed of 80kph. How long will it take for the car to overtake the truck?
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A quick and short "naive" solution
In 20 minutes, a truck is  = 20 km ahead the car.
Moving faster than the truck, the car has approaching speed of 80-60 = 20 km/h.
Therefore, it is clear that the car will overtake the truck in  = 1 hour. ANSWER
A slow Algebra solution
Let t be the time after the car started.
So, to the catching moment, the car moves t hours.
The truck started 20 minutes earlier, so the truck moved (t+1/3) hours till the car catches up the truck.
They cover the same distance, so we write this distance equation
80*t = 60*(t+1/3)
Left side is the distance covered by the car; right side is the distance covered by the truck.
To solve, multiply both sides of the equation by 3. You will get
240t = 60*(3t+1)
Simplify and find t
240t = 180t + 60
240t - 180t = 60
60t = 60
t = 60/60 = 1 hour.
So, the car overtakes the truck in 1 hour after the car' start.
You get the same answer.
Solved (in two different ways for your better understanding).
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- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
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Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
kph = kilometers per hour
60 kph = (60 km/1 hr)*(1 hr/60 min) = 1 km per min
80 kph = (80 km/1 hr)*(1 hr/60 min) = 4/3 km per min
Divide the kph value by 60 to convert to km per min.
In short,
60 kph = 1 km per min
80 kph = 4/3 km per min
x = amount of time, in minutes, the car has driven
The truck got a 20 minute head start, so it has traveled 20 minutes longer compared to x.
x+20 = amount of time, in minutes, the truck has driven
The truck drives at a speed of 1 km per min, so it travels a distance of 1*(x+20) = x+20 kilometers
Use the formula
Distance = rate*time
Meanwhile, the car travels (4/3)x kilometers
Summary table so far
| Vehicle | Distance (km) | Rate (km per min) | Time (minutes) | | Car | (4/3)x | 4/3 | x | | Truck | x+20 | 1 | x+20 |
The vehicles meet up when they have traveled the same distance.
Equate those two distance expressions and solve for x.
Car's distance = Truck's distance
(4/3)x = x+20
4x = 3(x+20)
4x = 3x+60
4x-3x = 60
x = 60
This is the amount of time, in minutes, needed for the car to meet up with the truck. Shortly afterward the car overtakes the truck.
Both vehicles travel 80 km when the two have met up.
Answer: 1 hour
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