Question

Working alone, it would take Shandra 45 minutes to mow the lawn. To mow the same lawn, also working alone, it would take Kelly 1 hour and 15 minutes. If they work together, the girls believe it will take them 1 hour to mow the lawn. 

Which best describes the reasonableness of their solution?  Their estimate is longer than the time it will actually take: 

Their estimate is accurate:  Their estimate is shorter than the amount of time it will actually take:  Their estimate is longer than the time it will actually take: 

Answer 1

The correct answer is:

Their estimate is longer than the time it will actually take.

( Since, Estimated time-- 1 hour=60 minutes

Time actually taken= 28.125 minutes )

Step-by-step explanation:

Time taken by Shandra alone to mow the field is: 45 minutes.

Time taken by Kelly alone to mow the field is: 1 hour 15 minutes.

We know that:

1 hour=60 minutes

Hence, 1 hour 15 minutes=60 minutes +15 minutes=75 minutes.

By looking at the time we consider that the total work be of 225 units.

This means that the Efficiency of Shandra is: 225/45=5 units/minutes.

Similarly,

Efficiency of Kelly is: 225/75=3 units/minutes.

• Now, when they will work together there efficiency will be added.

Hence, 5+3=8

Hence, the time taken by both of them when they work together is:

225/8

= 28.125 minutes.

But it was estimated that they took 1 hour=60 minutes.

Hence, there estimation of time taken was longer than what they actually took.

Answer 2

The correct answer is that their estimate is longer than the time it will actually take.

Step-by-step explanation:
Since Shandra can mow the entire lawn in 45 minutes, she can mow 1/45 of it in 1 minute.
Kelly mows the entire lawn in 1 hour 15 minutes, which is 75 minutes; this means she mows 1/75 of it in 1 minute.

Using these rates, and letting x be the amount of time it takes, we have the equation
1/45x + 1/75x = 1 (1 represents the entire lawn).

Rather than try to find a common denominator, we can "cancel" the denominators by multiplying everything by them. First multiply everything by 45:
45(1/45x)+45(1/75x)=1*45
1x+45/75x=45.

Now multiply everything by 75:
75(1x)+75(45/75x)=45*75
75x+45x=3375.

Combine like terms:
120x=3375.

Divide both sides by 120:
120x/120=3375/120
x=28.125.

It will take them a little over 28 minutes together, which means their estimate was longer than the actual time.