Question

A train covers 120 km at a uniform speed.
If its speed had been increased by 15 km/h,
it would have covered the distance in 40
minutes less. Find the original speed.​

Answer 1

Given:

• A train covers 120 km at a uniform speed
• If its speed had been increased by 15 km/h,  it would have covered the distance in 40 minutes less

To Find:

• Original speed of train

Solution:

Let the original speed of train be 'v km/h'

If we increase the speed of train by 15 km/h

Then, New speed= (v+15)km/h

Let the time taken by train to cover 120 km with original speed and new speed be t₁ hr and t₂ hr respectively

We know that,

$\longrightarrow\bf{Speed=\dfrac{Distance}{Time}}$

$\longrightarrow\bf{Time=\dfrac{Distance}{Speed}}$

Now,

Time taken by train to cover 120 km:

With Original speed

$\longrightarrow\mathrm{t_{1}=\dfrac{120}{v}}$

With New speed

$\longrightarrow\mathrm{t_{2}=\dfrac{120}{v+15}}$

According to question,

$\longrightarrow\mathrm{t_{1}-t_{2}=\dfrac{40}{60}}$

[Mins are converted into hours]

$\longrightarrow\mathrm{\dfrac{120}{v}-\dfrac{120}{v+15}=\dfrac{40}{60}}$

$\longrightarrow\mathrm{\cancel{120}\bigg(\dfrac{1}{v}-\dfrac{1}{v+15}\bigg)=\dfrac{\cancel{2}}{3}}$

$\longrightarrow\mathrm{60\bigg(\dfrac{v+15-v}{v(v+15)}\bigg)=\dfrac{1}{3}}$

$\longrightarrow\mathrm{180\bigg(\dfrac{15}{v^{2}+15v}\bigg)=1}$

$\longrightarrow\mathrm{\dfrac{2700}{v^{2}+15v}=1}$

$\longrightarrow\mathrm{2700=v^{2}+15v}$

$\longrightarrow\mathrm{v^{2}+15v=2700}$

$\longrightarrow\mathrm{v^{2}+15v-2700=0}$

$\longrightarrow\mathrm{v^{2}+60v-45v-2700=0}$

$\longrightarrow\mathrm{v(v+60)-45(v+60)=0}$

$\longrightarrow\mathrm{(v-45)(v+60)=0}$

$\longrightarrow\mathrm{v=45,-60}$

Since, speed can't be negative

∴ v= 45 km/hr

Hence, the original speed is 45 km/hr.

Answer 2

Answer:

45 km/h

Step-by-step explanation:

very easy refer to the picture attached

full answer step by step in the picture