Question

A bus leaves Los Angeles at 8am moving northeast at 60 mph. Three hours later, a truck leaves the same place traveling 1 2/3 times faster than the bus on the same route. How long will it take for the truck to catch up the bus?

Please show work

Answer 1

7.5 hours

Explanation:

Using the variable 't' for time, you can set up an equation to find out how long it will take the truck to catch up to the bus. Since the bus is traveling at 60mph and the truck is traveling 1 2/3 times faster, we need to first find the rate of the truck:

1
`(2)/(3)=(5)/(3)`

`(60)/(1)*(5)/(3)=(300)/(3)=100mph`

Using 't' and the knowledge that they will have traveled the same distance we the truck catches up to the bus and the fact that the truck left 3 hours later:

60t = 100(t - 3) or 60t = 100t - 300

Solve for 't': 60t - 100t = -300 or -40t = -300 so, t = 7.5 hours

Answer 2

The truck can catches the bus after 4.5 hours

Explanation:

As we know that speed of the bus is 60 mph

and The speed of the truck = 60 × =60 × = 100 mph

The bus moves before the truck by 3 hours

The bus moves a distance = 60 × 3 = 180 miles when the truck starts moving

So Distance of truck - Distance of bus = 180

Distance of truck = 100 × t = 100t

Distance of bus = 60 × t = 60t

so they meet each other at the same time

Now

100t - 60t = 180

40t = 180

t = 180/40 = 4.5

Now they meet each other after 4.5 hours

The truck can catches the bus after 4.5 hours