Question

A train from Portland, Oregon, to Los Angeles, California, travels at an average speed of 60 miles per hour and covers a distance of 963 miles. Susana is taking the train from Portland to Los Angeles to see her aunt. She needs to arrive at her aunts' house by 8 p.M. It takes 30 minuets to get from the train station to her aunt's house. What time does the train need to leave Portland for Susana to arrive by 8 p.M.

Answer 1

The train need to leave Portland at 03:27 am

Explanation:

step 1

Find out how long it takes the train to travel from Portland, Oregon, to Los Angeles, California

Remember that

The speed is equal to divide the distance by the time

so

The time is equal to divide the distance by the speed

Let

s ---> the speed in miles per hour

d ---> the distance in miles

t ---> the time in hours

`t=(d)/(s)`

we have

`d=963\ mi`

`s=60\ mi/h`

substitute

`t=(963)/(60)=16.05\ hours`

step 2

Adds 30 minutes (time it takes to get from the train station to her aunt's house)

Remember that

`30\ minutes=0.50\ hours`

`16.05+0.50=16.55\ hours`

Convert to minutes

`16.55\ h=16.55(60)\ min=993\ min`

step 3

Remember that

`8 p.m=20:00\ hrs`

Convert to minutes

`20(60)=1,200\ min`

Subtract 993 minutes from 1,200 minutes

`1,200-993=207\ min`

Convert to hours+minutes

`207\ min=207/60=3.45\ hours`

`0.45\ h=0.45(60)=27\ min`

so

`3\ h+27\ min`

`00:00 + 03:27=03:27\ am`

therefore

The train need to leave Portland at 03:27 am