Mark can clear a lot in 1.5 hours. his partner can do the same job in 3.5 hours. how long will it take them to clear the lot working together?

1.05 hours

Step-by-step explanation:

We need to use the least common multiple of 1.5 and 3.5 which is 10.5.

Thus we find how many lots each one will clear in 10.5 hours

Mart clears 1 lot in 1.5 hours

Number of Lots                 Time

           1                 ⇒           1.5 hours

so in 10.5 hous:

Number of Lots                 Time

           1                 ⇒           1.5 hours

           x                 ⇒           10.5 hours

the x is found by rule of three: multiply the cross quantities in the table (1 and 10.5) and dividing by the remaining amount (1.5):

x = 10.5*1/1.5

x = 7 lots

so Mark clears 7 lots in 10.5 hours.

His partner clears 1 lot in 3.5 hous:

Number of Lots                 Time

           1                 ⇒           3.5 hours

so in 10.5 hous:

Number of Lots                 Time

           1                 ⇒           3.5 hours

           x                 ⇒           10.5 hours

also by rule of three the x is:

x = 10.5*1/3.5

x = 3 lots

His partner clears 3 lots in the same 10.5 hours.

Thus, together:

Number of Lots                 Time

           7+3               ⇒        10.5 hours

simplifying:

Number of Lots                 Time

          10               ⇒        10.5 hours

and what we need to know is the time to clear one lot together:

Number of Lots                 Time

          10               ⇒        10.5 hours

          1                 ⇒        x

again, to find x we multiply cross quantities (10.5 by 1) and divide by the remaining amount (10):

x = 10.5*1/10

x = 1.05 hours

It will take them 1.05 hours to clear the lot

The correct answer is C (7, 9)

Firstly we know that each point is 6 away from the other in terms of x and in terms of y. Now we also know that for every 6, we will be one away from point B and five away from point A. We know this because the ratio is AB 5:1, meaning that the 5 is on the A side (they both come first).

So, we can just add 5 to each of the A value numbers to get point P.

A = (2, 4)

P = (2+5, 4+5)

P = (7, 9)