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Water is leaking from a tap at a rate of x cm³/min. (a) Write down an expression for the time taken to collect 50 cm of water. (b) When the tap is tightened, the water leaks at 3 cm/min less. Write down an expression for the time taken to collect the same amount of water. (c) The difference between the two times is 1.5 minutes. Form an equation in x and show that it reduces to x-3x-100 = 0.

Water is leaking from a tap at a rate of x cm³/min. (a) Write down an expression for the time taken to collect 50 cm of water. (b) When the tap is tightened, the water leaks at 3 cm/min less. Write down an expression for the time taken to collect the same amount of water. (c) The difference between the two times is 1.5 minutes. Form an equation in x and show that it reduces to x-3x-100 = 0.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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Water is leaking from a tap at a rate of x cm³/min. (a) Write down an expression for the time taken to collect 50 cm³ of water. (b) When the tap is tightened, the water leaks at 3 cm/min less. Write down an expression for the time taken to collect the same amount of water. (c) The difference between the two times is 1.5 minutes. Form an equation in x and show that it reduces to x-3x-100 = 0. (d) Solve this equation, giving your answers correct to 1 decimal place. (e) Hence, find the time taken to collect 50 cm of water, correct to the nearest second, before the tap is tightened.
Transcribed Image Text:Water is leaking from a tap at a rate of x cm³/min. (a) Write down an expression for the time taken to collect 50 cm³ of water. (b) When the tap is tightened, the water leaks at 3 cm/min less. Write down an expression for the time taken to collect the same amount of water. (c) The difference between the two times is 1.5 minutes. Form an equation in x and show that it reduces to x-3x-100 = 0. (d) Solve this equation, giving your answers correct to 1 decimal place. (e) Hence, find the time taken to collect 50 cm of water, correct to the nearest second, before the tap is tightened.
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