Question

A man traveling from A to B at 3 mph, takes half an hour rest at B, and returns to A at 5 mph. Total time taken is 3
hrs 26 min. find the distance from A to B.​

Answer 1

Answer:

Let the distance be 'x' km.

Therefore total time taken =

12

2x

+

15

x

hr

⇒ (

12

2x

+

15

x

)hr =42 min.

⇒ (

12

2x

+

15

x

) hr =

60

42

hr

12

2x

+

15

x

=

60

42

60

10x+4x

=

60

42

⇒ 14x=42

⇒ x=3

Total distance x=3 km

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Answer 2

Concept

Speed indicates how fast something or someone is moving. If you know the distance traveled by an object and the time it took to travel, you can find the average speed of that object.

 The formula for speed is speed = distance/time.

The formula follows and he can be changed in three ways.

•  speed = distance/time

•  distance = speed x time

•  time = distance/speed

To calculate one of the variables (speed, distance, or time) you need the other two.

For example, to find the time it takes to travel, we need the length of the trip and the speed of the trip.

Given

We have been given that speed of a man traveling from A to B is 3mph and takes half an hour rest at B and returns to A at 5 mph the time taken is 3hrs 26 minute .

Find

We are asked to determine the distance between A and B .

Solution

Let the distance between A and B be x m .

A man goes from point A to B with the speed of 3 m\hr.

A man comes from point B to A with the speed of 5m\hr.

Total time taken = 3 hours +26 minute

                            $=3\ hours +\frac{26}{60}hours\\\\=3\ hours +\frac{13}{30}hours\\\\=\frac{103}{30} hours$

As we know that  $Time=\frac{Distance}{Speed}$

According to the question, equation will be

$\frac{x}{3} +\frac{x}{5} =\frac{103}{30}\\\\\frac{5x+3x}{15} =\frac{103}{30}\\\\\frac{8x}{15} =\frac{103}{30}\\\\x=\frac{103\times 15}{30 \times8}\\\\\x=6.4375m$

Therefore, the distance between A and B is 6.4375m .

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