Question

A train travels 20km at a uniform speed of 60km / hr and the next 20km at a uniform speed at 60km/ hr and the next 20km at a uniform speed of 80km / h calculate it's average speed

Answer 1

Correct Question

A train travels 20 km at a uniform speed of 60 km/hr and the next 20 km at a uniform speed of 80 km/hr. Calculate it's average speed.

Solution-

Case 1)

A train travels 20 km at a uniform speed of 60 km/hr.

Time = Distance/Speed

t1 = 20/60 = 1/3 = 0.33 hr

Case 2)

The train travels next 20 km at a uniform speed of 80 km/hr.

t2 = 20/80 = 1/4 = 0.25 hr

Now,

Average speed is defined as the ratio of total distance covered with respect to total time taken.

Total distance covered = Distance covered in (first half + second half)

= (20 + 20) km

= 40 km

Total time taken = t1 + t2

= (0.33 + 0.25) hr

= 0.58 hr

Average speed = (Total distance covered)/(Total time taken)

Substitute the known values in the above formula,

Average speed = 40/0.58

= 68.96

= 69

Therefore, the average speed of the train in 69 km/hr.

Shortcut Method

Average speed = (2 × S1 × S2)/(S1 + S2)

= (2 × 60 × 80)/(60 + 80)

= 9600/140

= 68.57

= 69 km/hr (approx.)

Answer 2

Answer:

Given:

• A train travels 20km at a uniform speed of 60 km/hr and the next 20km at a uniform speed at 60 km/hr and the next 20km at a uniform speed of 80 km/hr.

Find:

• Calculate it's average speed.

Using formula:

★ ${\sf{\underline{\boxed{\red{\sf{Average \:speed = \dfrac{(2 \times S1 \times S2)}{(S1 + S2)} }}}}}}$

Calculations:

⇒ $\bold{(2 \times 60 \times 80) (60 + 80)}$

⇒ $\bold{\cancel{\dfrac{9600}{140}}}$

⇒ ${\sf{\underline{\boxed{\red{\sf{68.57 \: km/hr}}}}}}$

Therefore, 68.57 is it's average speed.