Easy math problem help...?

Whether it's "work," "washing" or some other task, you have to convert to a rate (speed), just as though you were traveling in a car at so many mph, and you want to know how long it will take to reach your destination.

Let the rates be designated as m, s, b and y (mom, sis, brother and you). Your mom washes 1 car in 4 minutes, which equates to (1/4) car/minute.

m = (1/4)

s = (1/6)

b = (1/8)

y = (1/10)

The sum of the products of rate and time, t, must equal 1.

(1/4 + 1/6 + 1/8 + 1/10)t = 1 select a common denominator: 120

1/4 = 30/120; 1/6 = 20/120; 1/8 = 15/120; 1/10 = 12/120

(30 + 20 + 15 + 12)/120 x t = 1 = 77t/120

t = 120/77 minutes. Your answer is correct.

Yes, you got the right answer.

If your mom can wash the car in 4 minutes, that means she washes 1/4 of the car every minute. Likewise, sister washes 1/6th, brother 1/8th, and you 1/10th every minute. So the rate with everyone working is

1/4 + 1/6 + 1/8 + 1/10

Lowest common denominator is 120:

( 30 / 120 ) + ( 20 /120 ) + ( 15 / 120 ) + ( 12 / 120 ) = 77 / 120

That's the rate. So the time is one over that, or 120 / 77, as you found.

Good work!

Express everyone's rate in terms of cars per minute then add...

1/4 + 1/6 +1/8 + 1/10 = 30/120 + 20/120 + 15/120 + 12/ 120 = 77/120

Time for the group to wash a car is 120/77 = 1.558 minutes or 1 minute 33.5 seconds

10 surely as it should only take as long as the longest person takes

ANS: your answer is right!