Question

acme movers charges $150 plus $30 per hour to move household goods across town. hanks movers charges $55 per hour. for what lengths of time does it cost less to hire banks movers?

Answer 1

For the length of time less than 6 hours cost less to hire Hanks movers

Explanation:

Let

x -----> the time in hours

y ----> the total cost in dollars

we know that

Acme movers

`y=30x+150` ----> equation A

Hanks movers

`y=55x` ----> equation B

Equate equation A and equation B and solve for x

`55x=30x+150`

`55x-30x=150`

`25x=150`

`x=6\ hours`

That means-----> For x= 6 hours The cost in both companies is the same

Verify

For x=6 hours

Acme movers

`y=30(6)+150=\$330`

Hanks movers

`y=55(6)=\$330`

If x < 6 hours ----> It cost less to hire Hanks movers

If x > 6 hours ----> It cost less to hire Acme movers

therefore

For the length of time less than 6 hours cost less to hire Hanks movers