EASY MATH QUESTION THAT I CAN'T DO?

Recall: s = d/t → where s is the speed, d is the distance, t is the time


First stage:

If half the distance was travelled at an average of 100 km/h (...)

s₁ = d₁/t₁

t₁ = d₁/s₁ → where: d₁ = d/2

t₁ = (d/2)/s₁ → where: s₁ = 100

t₁ = d/200


(…) and the other half an average speed of 60 km/h (…)

s₂ = d₂/t₂

t₂ = d₂s₂ → where: d₂ = d/2

t₂ = (d/2)/s₂ → where: s₂ = 60

t₂ = d/120



A certain journey took 40 minutes to complete.

t = t₁ + t₂

t = (d/200) + (d/120)

t = (3d/600) + (5d/600)

t = 8d/600

t = d/75 → recall: t = 40 minutes → you know that: 40 min = (40/60) hour = (4/6) hour = (2/3) hour

d/75 = 2/3

d = 75 * (2/3)

d = 150/3

d = 50 km

Let y km be the length of the whole journey.

Time taken for the first half the distance = (y/2 km) / (100 km/h) = y/200 h
Time taken for the second half the distance = (y/2 km) / (60 km/h) = y/120 h

Total time taken for the journey (in h) :
(y/200) + (y/120) = 40/60
[(y/200) + (y/120)] * 200 * 120 = (40/60) × 200 × 120
120y + 200y = 16000
320y = 16000
y = 50

The length of the whole journey = 50 km

Total time = 40 minutes = 0.666 hours

x --> Half of the total distance.
t --> Time needed to travel the first half.

x = v * t
x = 100 * t
x = 60 * (0.666 - t) = 39.96 - 60t

100t = 39.96 - 60t
160t = 39.96
t = 39.96 / 160
t = 0.249 h

x = 100 * t
x = 100 * 0.249
x = 24.975 km

Total length = 2 * 24.975 = 49.95 km --> 50 km

Total distance = d
t1 = d/2 / 100 = d / 200 h
t2 = d/2 / 60 = d / 120 h

2/3 = d/200 + d/120
1600 = 12 d + 20 d
400 = 3 d + 5d
d = 50 km

Thanks for the help everyone!!!!!!!

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