Question

You and your college roommate travel to your respective hometowns in the same amount of time. You drive 230 miles and your friend drives 210 miles. Your friend's average speed is 6 miles per hour lower than your average speed. What is your average speed?

Answer 1

69 miles per hour is your average speed and your roommate average speed is 63 miles per hour.

Explanation:

The given is,

Same amount of time

You drive 230 miles

Your roommate drive 210 miles

Average speed of your roommate is 6 miles per hour lower than your average speed.

Step:1

Let, x - Your average speed ( miles/hour)

From given,

Average speed of your roommate = x - 6

Step:2

Time taken by you =
`(Total distance)/(Average speed)`

=
`(230)/(x)`

Time taken by your roommate =
`(Total distance)/(Average speed)`

=
`(210)/(x-6)`

Step:2

From given,

Time taken by you = Time taken by yours roommate.....(1)

`(230)/(x)` =
`(210)/(x-6)`

(x-6) (230) = (x) (210)

( 230x - 1380 ) = 210x

230x - 210x = 1380

20x = 1380

x =
`(1380)/(20)`

x = 69

From the x value,

Your average speed, x = 69 miles per hour

Average speed of your roommate = 69 - 6 = 63 miles per hour

Step:4

Check for answer,

Time taken by you =
`(230)/(x)` =
`(230)/(69)` = 3.333 hours

Time taken by your roommate =
`(210)/(x-6)` =
`(210)/(63)` = 3.33 hours

From equation (1)

3.333 = 3.333

Result:

69 miles per hour is your average speed, if You and your college roommate travel to your respective hometowns in the same amount of time. You drive 230 miles and your friend drives 210 miles. Your friend's average speed is 6 miles per hour lower than your average speed.