Question

If a boat goes upstream at a speed of 24 km/hr and comes back the same distance at 40 km/hr. What is the average speed (in km/hr) for the total journey.

Answer 1

Answer:

Given:

Upstream speed = 24 km/hr

Downstream speed = 40 km/hr

To find:

Average speed of the boat during the journey

Concept:

Average speed is the ratio of total distance to the total time. We know the total distance.

We just need to find the total time.

Calculation:

Let the distance for each journey = L

So, total distance

= upstream dist. + downstream dist.

= L + L

= 2L

Now total time can be calculated as follows:

Time for upstream journey = L/24 hr.

Time for downstream journey = L/40 hr.

So total time = L/24 + L/40

=> total time = (5L + 3L)/120 hr.

=> total time = (8L/120) hr.

Average speed = Distance/time

=> avg. speed = 2L/(8L/120)

=> avg. speed = 30 km/hr.

So the answer is 30 km/hr.

Answer 2

Answer :-

$\rightarrow \boxed{ \sf{ average \: speed \: (v) = 30 \: \frac{km}{hr} }} \:$

To Find :-

→ Average speed

Formula used :-

$\star \: \: \boxed{ \sf{ average \: speed = \frac{ distance}{total \: time} } }$

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Step - by - step explanation :-

according to the question,

• Upstream speed of boat = 24 km/hr

• downstream speed of boat = 40 km/hr

Let distance traveled by boat is "d",

when boat goes Upstream then it travel "d" distance ,

so distance goes downstream is also "d"

hence,

total distance traveled by boat = 2d

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→ when goes to upstream ,

Time = distance /speed = d/24 hr

→ when goes to downstream

Time = d/40 hr

hence,

total time taken by boat

$\rightarrow \sf{ \frac{d}{24} + \frac{d}{40} } \\ \\ \rightarrow \sf{ \: \frac{5d + 3d}{120} } \\ \\ \rightarrow \: \sf{ \frac{8d}{120} } \\ \\ \rightarrow \: \sf{total \: time = \frac{d}{15} hr}$

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Therefore ,

$\rightarrow \sf{average \: speed(v) = \frac{total \: distance}{total \: time} } \\ \\ \rightarrow \sf{ \: v = \frac{2d}{ \frac{d}{15} } \: \frac{km}{hr} } \\ \\ \rightarrow \boxed{ \sf{ average \: speed \: (v) = 30 \: \frac{km}{hr} }}$

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