Question

Karim, a tourist leaves ellora on a bicycle. Having travelled for 1.5 h at 16 km/h, he makes a stop for 1.5 h and then pedals on with the same speed. Four hours after karim started, his friend and local guide rahim leaves ellora on a motorcycle and rides with a speed of 28 km/h in the same direction as karim had gone. What distance will they cover before rahim overtakes karim?

Answer 1

Answer:

In the first 1.5hr Karim covered a distance= 16*1.5= 24km

He stopped for 1.5 hrs

So by now he has taken 3hrs

In the next 1hr he will cover 16*1 =16km

so in total he covered 40kms before Rahim started.

the relative speed between raheem and Karim is 28-16= 12km/hr (as they are travelling in same direction so relative speed is the difference of two speeds)

at what distance Rahim overtakes kareem =(distance by which first person is already ahead/ relative Speed)* speed of 2nd person

= (40*28)/12 =9.33kms

Answer 2

They travel 93.33 kms before Rahim overtakes Karim.

According to the question, Karim left Ellora with:

Speed = v = 16km/hr

Time= t = 1.5 hours

So, the distance he travelled = S = vt

S= 16×1.5 = 24km.

Now, he rests for 1.5 hours. So, 3 hours passed and he travelled 24 km.

Four hours after he started, i.e. one hour after he started pedaling again, Rahim set off from Ellora.

Now, one hour passed.

Speed of Karim = v = 16km/hr

Time= t = 1 hr

Distance he travelled in one hour after he started pedaling again = S = vt

S= 16×1 = 16 km.

After four hours, i.e. at the time Rahim started, Karim travelled a distance of 24+16 = 40km.

Now, before Rahim manages to overtake Karim, Karim will travel some distance after travelling 40km. Let that distance be x. So, the time Rahim will take to cover the entire distance and the distance Rahim will take to travel distance 'x' will be the same.

Take 'x'.

Distance = x = Speed of Karim (v) × time (t)

x = 16t-------------- [I]

Now, the distance travelled by Rahim = Y = 40+x ---------[II]

Y=  Speed of Rahim × time (t)

Y = 28t ------------ [III]

Substituting [III] in [II],

28t = 40+x ------------ [IV]

Substituting [I] in [IV],

28t = 40+16t

12t = 40

t = $\frac{40}{12}$ = $\frac{10}{3}$

Hence, t = $\frac{10}{3}$ hours ------------------ [V]

Now, substituting [V] in [I],

x= 16×$\frac{10}{3}$

x = $\frac{160}{3}$

x = 53.33 km ------------------------ [VI]

Substituting [VI] in [II],

distance travelled by Rahim = Y = 40+53.33

= 93.33 km.

Therefore, they will travel 93.33 km before Rahim overtakes Karim.