Pregunta
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Question 2
The time (t) taken to buy a fuel at a petrol station variation varies directly as the number of vechice on a quene and inwersely as the number of pumps § available in a station. In a station of 5 pumps, it took 10 minutes to fuel 20 vechiles
Find;
(a) The relationship betweet and .
(b) The time it will taple to fuel 50 vechiles in Station usithe 2 pumps

Ask by Bright Montgomery. in Ghana
Jan 23,2025

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(a) The relationship is .
(b) It will take 62.5 minutes to fuel 50 vehicles with 2 pumps.

Solución

Let’s solve the problem step by step.

Given:

  • Direct Variation: Time varies directly with the number of vehicles .
  • Inverse Variation: Time varies inversely with the number of pumps .

(a) Establishing the Relationship Between , , and

When a variable varies directly with one variable and inversely with another, the relationship can be expressed as:
Where:
  • = Time taken to fuel the vehicles
  • = Number of vehicles in the queue
  • = Number of pumps available
  • = Constant of proportionality
So, the relationship is:

(b) Calculating the Time to Fuel 50 Vehicles with 2 Pumps

Step 1: Find the Constant Using Given Data
Given:
  • pumps
  • vehicles
  • minutes
Plug these values into the relationship:
Step 2: Use to Find the Time for Vehicles and Pumps
Plug , , and into the relationship:
Therefore, it will take 62.5 minutes to fuel 50 vehicles using 2 pumps.

Summary

  • (a) The relationship is .
  • (b) It will take 62.5 minutes to fuel 50 vehicles with 2 pumps.

Respondido por UpStudy AI y revisado por un tutor profesional

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The Deep Dive

When you’re dealing with direct and inverse variations, think of it like a balancing act! In this scenario, the relationship can be expressed using the formula , where is a constant. Given that it took 10 minutes for 20 vehicles at 5 pumps, we can first find the constant . Plugging the values in, we get , which simplifies to . Now we have our relationship!
For the second part, we want to find out the time for 50 vehicles at 2 pumps. Using the same formula , substitute and : minutes. So, buckle up; it will take about 62.5 minutes to refuel those vehicles with only 2 pumps available!

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