Question

bob and ross are both work as painters. bob can paint 2 rooms in 130 minutes, and ross can paint 3 rooms in 170 minutes. at this rate, if bob and ross each work 10 hour shifts, many days will it take bob and ross to paint a 200 room apartment complex? days =

Explanation:

Step1: Calculate Bob's rate per minute

Bob can paint 2 rooms in 130 minutes, so his rate $r_{Bob}=\frac{2}{130}=\frac{1}{65}$ rooms per minute.

Step2: Calculate Ross's rate per minute

Ross can paint 3 rooms in 170 minutes, so his rate $r_{Ross}=\frac{3}{170}$ rooms per minute.

Step3: Convert 10 - hour shift to minutes

Since 1 hour = 60 minutes, a 10 - hour shift is $10\times60 = 600$ minutes.

Step4: Calculate the number of rooms Bob paints in a 10 - hour shift

The number of rooms Bob paints in 600 minutes is $n_{Bob}=r_{Bob}\times600=\frac{1}{65}\times600=\frac{120}{13}$ rooms.

Step5: Calculate the number of rooms Ross paints in a 10 - hour shift

The number of rooms Ross paints in 600 minutes is $n_{Ross}=r_{Ross}\times600=\frac{3}{170}\times600=\frac{180}{17}$ rooms.

Step6: Calculate the total number of rooms they paint together in a 10 - hour shift

$n = n_{Bob}+n_{Ross}=\frac{120}{13}+\frac{180}{17}=\frac{120\times17 + 180\times13}{13\times17}=\frac{2040+2340}{221}=\frac{4380}{221}\approx19.82$ rooms.

Step7: Calculate the number of days

To paint 200 rooms, the number of days $d=\frac{200}{n}=\frac{200\times221}{4380}=\frac{44200}{4380}\approx10.1$ days. Since we need to complete the job, we round up to 11 days.

Answer:

11