How long will it take a bus traveling at 60 miles per hour to overtake a car traveling at 40 mph if the car had a 1.5 hour head start?
let the time it takes for the bus to catch up to the car be t hours
So the bus went 60t miles
but meantime, the car went for t+1.5 hours at 40 mph for a distance of 40(t+1.5
But when the bus catches up to the car, haven't both gone the same distance ??
so
60t = 40(t+1.5)
60t = 40t + 60
20t = 60
t = 3
so it will take 3 hours
check: in 3 hours the bus went 3(6) = 180 miles
the car went for 4.5 hrs at 40 = 180 miles
Checks out !!!
A kayak was reduced from $750 to $600, what percentage was it reduced?
To find out how long it will take the bus to overtake the car, we need to determine the time it takes for the bus to cover the distance that the car has already traveled during its head start.
Let's break down the problem:
1. Calculate the distance traveled by the car during its 1.5-hour head start:
Distance = Speed * Time
Distance = 40 mph * 1.5 hours
Distance = 60 miles
2. Now that we know the distance between the two vehicles is 60 miles, we can find out how long it will take the bus to cover this distance while traveling at 60 mph:
Time = Distance / Speed
Time = 60 miles / 60 mph
Time = 1 hour
Therefore, it will take the bus 1 hour to overtake the car.
distance = rate x time
Let t = time bus travels
then t+1.5 hours = time car travels
60t = distance traveled by bus.
40(t+1.5) = distance traveled by car.
distance traveled by bus = distance by car.
60t = 40(t+1.5)
solve for time, then use
d = rt to determine the distance.