Question
Two window washers start at the heights shown ,one is rising , other is descending . How long does it take for the two window washers to reach the same height ? Explain.
Hint:
1. Speed =
2. 1 foot = 12 inches
3. New height = Current height (+/-) distance travelled by the window washer.
The correct answer is: After 18.32 seconds, the two window washers will reach the same height.
Step-by-step solution:-
Let the 2 window washers be w1 & w2, respectively and the time taken by them be x sec
As per the given diagram, we get-
Current height of w1 = 21 ft.
∴ Current height of w1 = (21 × 12) inches ................................ (1 foot = 12 inches)
∴ Current height of w1 = 252 inches ........................................ (Equation i)
Speed of w1 = 8 in./sec
Current height of w2 = 50 ft.
∴ Current height of w2 = (50 × 12) inches ................................ (1 foot = 12 inches)
∴ Current height of w2 = 600 inches ........................................ (Equation ii)
Speed of w2 = 11 in./sec
We know that-
Distance covered by w1 upwards = current speed × time ............................. (Speed = Distance/Time)
∴ Distance covered by w1 upwards = 8 × x
∴ Distance covered by w1 upwards = 8x ................................... (Equation iii)
New height of w1 = current height of w1 + distance covered upwards
∴ New height of w1 = 252 + 8x .................................................. (From Equations i & iii) ....................................... (Equation iv)
Distance covered by w2 downwards = current speed × time ............................. (speed = )
∴ Distance covered by w2 downwards = 11 × x
∴ Distance covered by w2 downwards = 11x ................................... (Equation v)
New height of w2 = current height of w2 - distance covered downwards
∴ New height of w2 = 600 - 11x .................................................. (From Equations ii & v) ........................................ (Equation vi)
Now, we need to find the value of x for which the 2 window washers will be at the same height.
∴ New height of w1 = New height of w2
∴ 252 + 8x = 600 - 11x ….............................. (From Equations iv & vi)
∴ 11x + 8x = 600 - 252 ................................. (Taking variables & constants on either sides of the equation)
∴ 19x = 348
∴ x = 
∴ x = 18.32 sec
Final Answer:-
∴ After 18.32 seconds, the two window washers will reach the same height.
The rate at which an object move is refers as its speed. If an object has traveled far away from the initial place and how much time it takes? To be calculated using the average speed traveled by an object. The speed formula is speed = distance/time. To determine the units for speed, we must consider the units for distance and time.
There are three different ways to write the formula. They are:
• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
Here speed, distance, and time are internally linked. So, to calculate the value of among one, we require another unit.
For example, to determine the time required to complete a journey, we must know the distance and speed first.
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