Question

The distance between two cities a and b is 80 km. A motorcycle rider starts from a towards b at 7 am with a speed of 10 km/hr. Another motorcyclist starts from b towards 8 am with a speed of 25km/hr. At what time will they cross each other?

Answer 1

Suppose they meet x hrs after 8 a.m.

then

(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]

= 330

So, 60x+75(x-1) = 330

x=3.

So,they meet at (8+3). i.e 11a.m.

Answer 2

Given:

• Distance between two cities A and B = 80 Km.
• Time taken by the first motorcycle to travel from A to B  = 1 hour.
• Speed of the first motorcycle = 10 Km/hr.
• Speed of the second motorcycle = 25Km/hr.

To Find:

• Time when both the motorcycle will cross each other.

Solution:

• From the given data we get to know the distance covered by the first motorcycle from 7 am to 8 am is 10 Km.
• The remaining distance is 80 - 10 = 70 Km.
• We get the relative speed of both the motorcycles as they are traveling opposite to each other, 10+25 = 35Km/hr.
• Time taken = $\frac{distance}{relative speed}$ = $\frac{70}{35}$ hours.
• T = 2 hours. = 2+1 = 3hrs.
• So both the motorcycles will meet each other after 3 hours from 7 am, they will meet at 10 am.

At 10 am, both the motorcycles will cross each other.