Question

Two cats start from opposite ends of an 8 mile road, driving towards eachother. One car is driving at a rate of 4mph and the other is driving at a rate of 6 mph. After how long will the cars meet

Answer 1

The cars will meet each other after 0.8 hour [48 minutes]

Explanation:

* Lets explain how to solve the problem

- The two cars start from opposite ends of a 8 mile rode

# The distance between them is 8 miles

- The two cars driving towards each other

# the time for both same

- One car is driving at a rate of 4 mph

# The rate of the car is 4 miles per hour

- Other car is driving at a rate of 6 mph

# The rate of the car is 6 miles per hour

- We need to know they will meet each other after what time

- They move towards each other and meet each other after t hour

and the total distance d is the sum of the two car's distances

`d_(1)` and
`d_(2)` ,this total distance is 8 miles

∴ d =
`d_(1)` +
`d_(2)`

∵ d = 8

∴
`d_(1)` +
`d_(2)`

- Distance = rate × time

∵ The rate of one care is 4 mph

∵ The rate of the other car is 6 mph

∵ The time for both cars is t

∴
`d_(1)=4t` and
`d_(2)=6t`

- Substitute these values in the equation above

∴ 4t + 6t = 8

∴ 10t = 8

- Divide both sides by 8

∴ t = 0.8

∴ The cars will meet each other after 0.8 hour [48 minutes]