Practice Question 3

Question

Elinnah can mow her lawn in 3 hours and her brother, Oseko, can mow it in 2 hours only. How long will it take them to mow their lawn if they work together?

A. 1 hour 20 minutes

B. 1 hour 15 minutes

C. 1 hour 12 minutes

D. 1 hour 35 minutes

E. 1 hour 30 minutes

Answer 1

WHAT DO WE KNOW?

Elinnah can mow her lawn in 3 hours.-----That means in 1 HOUR she mows 1/3 of the lawn

Oseka can mow the same lawn in 2 hours.----That means in 1 HOUR he mows 1/2 of the lawn.

HOW MUCH GETS DONE IN ONE HOUR?

This means if both of them are mowing the lawn at the same time, then in 1 hour:

Elinnah would complete 1/3 of the lawn & Oseka would complete 1/2 of the lawn

1/3 + 1/2 = 5/6

So in 1 hour with their combined effort , 5/6 of the lawn would get mowed.

WHAT WE NEED TO FIND OUT?

We need to find out how much time it will take to mow the lawn if both are mowing at the same time.

Let's call the total time "t" hours.

SOLUTION:

In 1 hour-----> 5/6 of the lawn is completed

In "t" hours-------> 5/6 multiplied by "t" , the full lawn is completed.

So, 5/6t = 1

Multiply both sides by 6:

6 x 5/6 t= 1 x 6

5t=6

Divide both sides by 5:

5t/5 = 6/5

t=6/5 hours

t= 1.2 hour

We need to convert .2 hours into minutes.

1hour ------> 60 minutes.

.2 hours -----> .2 x 60 minutes

.2 x 60 = 12

So the total time needed to mow the lawn with both Elinnah and Oseka mowing together is :

1 hour and 12 minutes

Answer 2

t represents the time working together.

(t / 3) + (t / 2) = 1

2t + 3t = 6

5t = 6

t = 1.2 hours.

Answer 3

Patrick F.'s solution is clear and correct.

For additional learning:

this kind of work problem is often set up as (1/3)+(1/2)=(1/x) and the answer is exactly what Patrick showed.

As Patrick's explanation shows the reciprocal of the time given in the problem is a RATE...amount of the whole lawn per hour.

Answer 4

Let's think about how much they can mow together for one hour.

In one hour Elinnah can mow 1/3 of the lawn and Oseko can mow 1/2 of the lawn.

Together they can mow 1/3 + 1/2 = 5/6 of the lawn.

Now we can set up a ratio:

5/6 : 1 hr

1 : x hr (that's 1 for 1 full lawn)

Cross multiply and get this equation: 5/6 x = 1 => x = 6/5 = 1 and 1/5 hr = 1 hr 12 min