Pregunta
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
The time (t) taken to buy a fuel at a petrol station variation varies directly as the number of vechice
Find;
(a) The relationship betweet
(b) The time it will taple to fuel 50 vechiles in Station usithe 2 pumps
Ask by Bright Montgomery. in Ghana
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
(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
Como
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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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