How long will it take for a car that is traveling at 60 mph to overtake a bus that is traveling at 50 mph if the bus had a 2-hour head start?
The bus is 100 miles ahead. The relative speed advantage is (60-50)mph.
time=distance/relativevelocity= 10 hrs.
12
To determine how long it will take for the car to overtake the bus, we need to calculate the time it takes for the car to cover the distance that is equal to the initial head start of the bus.
To do this, we can use the formula:
Time = Distance / Speed
Let's denote:
Distance covered by the car to overtake the bus = x (miles)
Time taken by the car to travel x miles = t (hours)
Given that the car is traveling at 60 mph and the bus is traveling at 50 mph, we know their speeds.
First, let's calculate the distance the bus traveled during its head start.
Speed of the bus = 50 mph
Time taken by the bus = 2 hours
Distance covered by the bus during its head start = Speed of the bus * Time taken by the bus = 50 mph * 2 hours = 100 miles
Now, we need to find the time it will take for the car to cover the distance of 100 miles (distance covered by the bus during its head start).
Using the formula:
Time = Distance / Speed
t = x / 60
We know that the car will be traveling for t hours, and during this time, the bus will also be traveling for t + 2 hours (accounting for the initial head start).
The distance covered by the car during t hours = Speed of the car * t = 60 mph * t = 60t miles
Since we want the car to cover the same distance as the bus's head start, we can set up an equation:
60t = 100
Now we can solve for t:
t = 100 / 60
t ≈ 1.67 hours
Therefore, it will take approximately 1.67 hours (or 1 hour and 40 minutes) for the car traveling at 60 mph to overtake the bus traveling at 50 mph, given the bus had a 2-hour head start.