Question

A motorcyclist rode the first half of his way at a constant speed. then he was delayed for 5 minutes and, therefore, to make up for the lost time he increased his speed by 10 km/h. find the initial speed of the motorcyclist if the total path covered by him is equal to 50 km. (1) 36 km/h (2) 48 km/h (3) 50 km/h (4) 62 km/h

Answer 1

v₁ = speed in first half

D = total distance traveled = 50 km

d₁ = distance of the first half = 25 km

t₁ = time taken in first half

t₁ = d₁ /v₁

t₁ = 25/v₁                                                 eq-1

for the second half :

v₂ = speed in second half = v₁ + 10

d₂ = distance of the second half = 25 km

t₂ = time taken in second half

t₂ = d₂ /v₂

t₂ = 25/(v₁ + 10)                                           eq-2

given that :

t₁ - t₂ = 5/60                        (5 min in h = 5/60 h)

(25/v₁ ) - (25/(v₁ + 10)) = 5/60

v₁ = 50 km/h

Answer 2

The initial speed of a motorcyclist is $50 km/h$.

The formula of time :

$t = d/s$

Explanation of solution :

For the first half -

• $s1 =$ speed of the first half.
• $D =$ total distance traveled $= 50 km$.
• $d1 =$ distance of the first half $= 25km$.
• $t1 =$ time taken in the first half.
• $t1 = d1/s1$
• $t1 = 25/s1$

For the second half -

• $s2 =$ speed in the second half $= v1 + 10$.
• $d2 =$ distance of the second half $= 25km$.
• $t2 =$ time taken in the second half.
• $t2 = d2/s2$
• $t2 = 25(s1 + 10)$

Given that :

$t1 - t2 = 5/60$

$(25/s1) - (25/(s1 + 10)) = 5/60$

$s1 = 50 km/h$

Therefore, the initial speed of a motorcyclist is $50 km/h$.

#SPJ2