Question

it takes mike 1 hour to get to work each day. he first rides the train, which travels at an average rate of 65 miles per hour.

Answer 1

6 minutes.

Step-by-step explanation:

Here is the complete question: It takes mike 1 hour to get to work each day. he first rides the train, which travels at an average rate of 65 miles per hour. Then he rides the subway train which travels at an average of 25 miles per hour. If the total distance that he travels from home to work is 61 miles. How many minutes does Mike spend riding the subway each morning?

Given: Total time taken by Mike is (t)= 1 hour

Average speed of train (s_1)= 65 miles per hour.

Average speed of subway train (s_2)= 25 miles per hour.

Total distance travel by Mike to reach office = 61 miles

Now, lets compute to find the time spend by Mike riding subway train.

Lets assume distance travel on train be `d`.

∴ distance travel on subway train is
`(61-d)\ miles`

Formula; Time=
`(distance)/(speed)`

Next, adding timing of travelling both on train and subway train to get 1 hour as given.

∴ 1 hours=
`(d)/(65) +((61-d))/(25)`

Taking LCD for both the fractions, we get 325

⇒ 1 hours=
`(5* d+ 13(61-d))/(325)`

Opening the parenthesis and distributing 13 with 61 and -d.

⇒ 1 hour=
`(5d-13d+793)/(325)`

⇒
`1 = (793-8d)/(325)`

Cross multiplying both side.

⇒
`1* 325= 793-8d`

subtracting both side by 325 and adding both side by 8d.

∴
`8d= 793-325`

cross multiplying

∴
`d= (468)/(8) = 58.5\ miles`

Distance travel on train is 58.5 miles.

∴ Distance travel in subway train is
`61-58.5= 2.5\ miles`

Distance travel on subway train is 2.5 miles.

Next finding time travelled on subway train.

`time= (distance)/(speed)`

`time= (2.5\ miles)/(25\ mph) = 0.10\ h`

coverting time unit in minutes.

remember, 1 hours= 60 minutes

∴ 0.10 hours=
`60 \ minutes * 0.10= 6\ minutes`

∴ Times taken by Mike to travel in subway train is 6 minutes.