a If someone washes a car in a minutes, then we can say that the rate is 1/a car per minute.
B
b Add together the expressions from Part A.
C
c Substitute 35 for x into the equation from Part B.
A
aFirst employee: 140 cars per minute
Second employee: 1x cars per minute Third employee: 1x+10 cars per minute
B
b R= x^2+90x+40040x(x+10) cars per minute
C
c R≈ 0.0758 cars per minute
About 4.5 cars per hour. See solution.
Practice makes perfect
a We know that someone washes a car in a minutes, so the rate is 1/a car per minute. We know that the first employee washes a car in 40 minutes, the second employee in x minutes, and the third employee in x+10 minutes.
Employee
Time to wash one car
Rate
First
40 minutes
1/40 car per minute
Second
x minutes
1/x car per minute
Third
x+10 minutes
1/x+10 car per minute
b We are asked to write a single expression R for the combined rate of cars washed per minute by the group. To do this, we will add the rates from Part A and then simplify.
Therefore, it represents R≈ 0.0758 car per minute. We are asked to find how many cars per hour this represents. Since we get 0.0758 car per minute, we will have 60 times more cars per hour.
0.0758 car per minute
⇕
60* 0.0758 cars per hour
⇕
4.5 cars per hour
