Question

Тому Сойєру було доручено пофарбувати паркан. Четверту частину роботи він виконав сам, потім передав пензлик Бену, який працював 15 хвилин, причому водив пензликом у два рази швидше, ніж Том. Після Бена за справу взявся Біл, який працював втричі швидше, ніж Том, та закінчив усю роботу за 5 хвилин. Скільки часу витратили хлопчики на фарбування всього паркану?

Answer 1

50 хвилин
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(15*2)+15+5

Answer 2

Problem Analysis

We are given that Tom was tasked with painting a fence. He completed one-fourth of the work himself, then passed the brush to Ben, who worked 15 minutes and painted twice as fast as Tom. Finally, Bill took over and completed the entire job in 5 minutes, working three times faster than Tom. We need to determine the total time spent by the boys on painting the entire fence.

Solution

Let's break down the problem step by step:

1. Tom completed one-fourth of the work, which means he painted 25% of the fence. 2. Ben took over and worked twice as fast as Tom. This means Ben painted 50% of the fence in 15 minutes. 3. Bill then completed the remaining work, which is 100% - 25% - 50% = 25% of the fence. 4. Bill worked three times faster than Tom, so he painted 3 * 25% = 75% of the fence in 5 minutes.

To find the total time spent by the boys on painting the entire fence, we need to add up the time spent by each boy.

1. Tom spent an unknown amount of time painting 25% of the fence. 2. Ben spent 15 minutes painting 50% of the fence. 3. Bill spent 5 minutes painting 25% of the fence.

Let's calculate the time spent by each boy:

1. Tom's time: Let's assume Tom's time is T minutes. Since he painted 25% of the fence, we can write the equation: T * (25/100) = 25/100. 2. Ben's time: Ben spent 15 minutes painting 50% of the fence, so his time is 15 minutes. 3. Bill's time: Bill spent 5 minutes painting 25% of the fence, so his time is 5 minutes.

Now, let's solve the equation for Tom's time:

T * (25/100) = 25/100

Simplifying the equation:

T = 25/100 * (100/25) = 1 minute

Therefore, Tom spent 1 minute painting 25% of the fence.

To find the total time spent by the boys, we add up the time spent by each boy:

Total time = Tom's time + Ben's time + Bill's time = 1 minute + 15 minutes + 5 minutes = 21 minutes

Therefore, the boys spent a total of 21 minutes painting the entire fence.

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