A motor car drives at an average speed of for 2 hours 45 minutes.
At which constant speed must the car drive to travel the same distance in
2 hours 35 minutes?
[20]
[4)

Ask by John Rodriguez. in South Africa

Mar 19,2025

Question

A motor car drives at an average speed of for 2 hours 45 minutes.
At which constant speed must the car drive to travel the same distance in
2 hours 35 minutes?
[20]
[4)

Ask by John Rodriguez. in South Africa

Mar 19,2025

UpStudy AI · Accepted Answer

To find the constant speed at which the car must drive to travel the same distance in 2 hours 35 minutes, we can use the formula:

$$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$

Given:
- Average speed of the car = $$ 106 \, \text{km/h} $$
- Time taken to travel the distance = 2 hours 45 minutes
- Time to travel the same distance at the constant speed = 2 hours 35 minutes

First, let's convert the time from hours and minutes to just hours:
- 2 hours 45 minutes = $$ 2 + \frac{45}{60} $$ hours = $$ 2 + 0.75 $$ hours = 2.75 hours

Now, we can calculate the distance traveled at the average speed:
$$ \text{Distance} = \text{Speed} \times \text{Time} = 106 \, \text{km/h} \times 2.75 \, \text{hours} $$

Next, we need to find the constant speed at which the car must drive to travel the same distance in 2 hours 35 minutes. Let's denote this constant speed as $$ S $$. The time to travel the same distance at the constant speed is 2 hours 35 minutes, which is $$ 2 + \frac{35}{60} $$ hours = $$ 2 + 0.5833 $$ hours = 2.5833 hours.

Now, we can set up the equation to find the constant speed $$ S $$:
$$ S = \frac{\text{Distance}}{2.5833 \, \text{hours}} $$

Let's calculate the constant speed $$ S $$.
Calculate the value by following steps:
- step0: Calculate:
  $$106\times 2.75$$
- step1: Multiply the numbers:
  $$291.5$$
The distance traveled at the average speed of $$ 106 \, \text{km/h} $$ for 2 hours 45 minutes is $$ 291.5 \, \text{km} $$.

Now, we can calculate the constant speed $$ S $$ at which the car must drive to travel the same distance in 2 hours 35 minutes:
$$ S = \frac{291.5 \, \text{km}}{2.5833 \, \text{hours}} $$

Let's calculate the constant speed $$ S $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{291.5}{2.5833}$$
- step1: Convert the expressions:
  $$\frac{\frac{583}{2}}{\frac{25833}{10000}}$$
- step2: Multiply by the reciprocal:
  $$\frac{583}{2}\times \frac{10000}{25833}$$
- step3: Reduce the numbers:
  $$583\times \frac{5000}{25833}$$
- step4: Multiply:
  $$\frac{583\times 5000}{25833}$$
- step5: Multiply:
  $$\frac{2915000}{25833}$$
The constant speed at which the car must drive to travel the same distance in 2 hours 35 minutes is approximately $$ 112.84 \, \text{km/h} $$.
The car must drive at approximately $$ 112.84 \, \text{km/h} $$ to travel the same distance in 2 hours 35 minutes.

A motor car drives at an average speed of for 2 hours 45 minutes.
At which constant speed must the car drive to travel the same distance in
2 hours 35 minutes?
[20]
[4)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Arithmetic Questions

A motor car drives at an average speed of for 2 hours 45 minutes. At which constant speed must the car drive to travel the same distance in 2 hours 35 minutes? [20] [4)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Arithmetic Questions

A motor car drives at an average speed of for 2 hours 45 minutes.
At which constant speed must the car drive to travel the same distance in
2 hours 35 minutes?
[20]
[4)