Don, Ric and Mike were in a committee to build a float for the homecoming parade. Each of them thoughtthat he could build it (continued...)alone in 16 hours. Don started work at 8:00 a.m., Ric...

Don, Ric and Mike were in a committee to build a float for the homecoming parade. Each of them thoughtthat he could build it (continued...)

alone in 16 hours. Don started work at 8:00 a.m., Ric at 8:30 a.m. and Mike at 9:00a.m. What time did they finish the float? (use one variable)

Use the format “Given, Required, Solution, Checking, Final Answer”

Asked on by spock7

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given:

Time needed for each to build alone = 16 hrs.

Don works at 8

Ric workds at 8:30

Mike works at 9:00

Required:

Time they finished the boat (T).

Solution.

If T is the time they all finish the boat, then, the total hours of work for the workers are:

Don works (T -8) hours.

Ric works (T-8.5) hours.

Mike workds (T-9) hours.

The works done for each in an hour = `1/16`  of the boat.

==> Now we will find the work done at T hour for each.

Don = `(T-8)*1/16 `

`` Ric = (`T-8.5)*1/16 `

`` Mike = `(T-9) * 1/16`

`` Then the total will be the finished boat = 1.

==> `(T-8)/16 + (T-8.5) /16 + (T-9)/16 = ` 1

==> T-8 + T- 8.5 + T-9 = 16

==> 3T -25.5 = 16

==> 3T = 41.4

==> T = `41.4/3`  = 13.8

Now we will convert to Time.

13 = 1 pm

0.8 = 0.8*60= 48 min.

Then , the time they finished the boat is 13:48 OR 1:48.

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