Question

Patty and Toby live 345 miles apart. They decide to drive to meet one another. Patty leaves at noon, traveling at an average rate of 45 mph, and Toby leaves at 3:00 P.M., traveling at an average speed of 60 mph. At what time will they meet?

Answer 1

5 P.M.

Explanation:

Distance= 345 miles.

Patty´s speed= 45 mph, started at 12 (noon)

Toby´s speed= 60 mph, started at 3 P.M.

∵ Patty have started 3 hour early at 12 noon.

∴ Patty have travelled (distance) =
`Speed* time`

=
`45* 3= 135\ miles`

Patty have already travelled 135 miles in 3 hours.

Remaining distance to be travelled by Patty and Toby=
`345 - 135= 210\ miles`

Remaining distance = 210 miles

Now, At 3 PM Toby have also started.

∴ Taking relative speed of Patty and toby=
`(45+60)= 105\ mph`

Next, finding time taken to meet each other.

`Time= (Distance)/(Speed)`

Time=
`(210)/(105) = 2\ h`

∴ After 2 hours they both meet each other, which is 5 P.M.