Question

9. A cyclist travels for 3 hours, covering for the first half of the journey at 12 km/h and the second half at
16 km/h. Find the total distance he covered.​

Answer 1

Answer:

total distance = 96 KM

Step-by-step explanation:

let total distance travelled = x

let time taken for first half = t

then time for second half = 3-t

then t*12+(3-t)*16=x  ...(1)

but t*12=x/2, t= x/24

putting this value of t in (1) and solving x=96 KM

Answer 2

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