Correct Answer - Option 2 : 336 kms
Given:
A cyclist travels for 15 hours, the first half at 21 km per hour and the second half at the rate of 24 km per hour
Let x be distance in km
Formula: Speed = (Distance ÷ Time)
Time T = 15 hours
The half distance (x/2) covered at 21 kmph in time T1.
The remaining half of the distance (x/2) covered at 24 kmph in time T2
Substitute the above values in the formula
⇒ 21 = (x/2) ÷ T1
⇒ 21 × T1 = x/2
⇒ 42 × T1 = x ------------1
⇒ 24 = (x/2) ÷ T2
⇒ 24 × T2 = x/2
⇒ 48 × T2 = x --------------2
Time T = T1 + T2 ⇒ 15 = T1 + T2 --------3
From 1 and 2 equations
⇒ 42 × T1 = 48 × T2
⇒ T1 ÷ T2 = 48 ÷ 42
⇒ T1 ÷ T2 = 8 ÷ 7
By equation 3
T1 = (15 × (8)) ÷ 15
T1 = 8 hours
T2 = 15 - 8 = 7 hours
By using the equation 1
⇒ 42 × 8 = x
⇒ x = 336 km
Hence, "336 kms" is the correct answer.
