Ramesh travels 760 km to his home, partly by train and partly by car. He takes 8 hours if he travels 160 km by train and the rest by car. He takes 12 minutes more if he travels 240 km by train and the rest by car. Find the speeds of the train and car separately.
Answers
Answer:
80 km/hr, 100 km/hr
Step-by-step explanation:
Let the speed of the train be x km/hr and car be y km/hr.
Total distance = 760.
(i)
Travels 160 km by train i.e (760 - 160) = 600 km by car and it takes 8 hours.
⇒ (160/x) + (600/y) = 8
Let (1/x) = u and (1/y) = v
⇒ 160u + 600v = 8
(ii)
Takes 12 minutes more if he travels 240 km by train i.e (760 - 240) = 520.
⇒ (240/x) + (520/y) = 8 + (12/60)
⇒ (240/x) + (520/y) = 492/60
⇒ (240/x) + (520/y) = 41/5
Let (1/x) = u and (1/y) = v
⇒ 240u + 520v = 41/5
On solving (i) * 6 & (ii) * 4, we get
960u + 3600v = 48
960u + 2080v = 164/5
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1520v = 76/5
v = 1/100
v = (1/100) => y = 100
Substitute v = (1/100) in above equations, we get
⇒ 240u + 520v = 41/5
⇒ 240u + 520(1/100) = 41/5
⇒ 240u + (52/10) = 41/5
⇒ 240u = (41/5) - (52/10)
⇒ 240u = 3
⇒ u = 1/80
u = (1/80) ⇒ x = 80
Therefore:
Speed of the train = 80 km/hr
Speed of the car = 100 km/hr
Hope it helps!
Let the speed of train = x km/hr and speed of car= y km/hr
Case 1
Distance travelled by train = 160 Km
Distance travelled by car = 760-160 = 600
kmTime taken by train = 160/x hr
Time taken by car = 600/y hr
Total time taken = 160/x+600/y hr160/x+600/y = 8 --------------- Equation 1
Case 2
Distance travelled by train = 240 Km
Distance travelled by car = 760-240 = 520 km
Time taken by train = 240/x hr
Time taken by car = 520/y hr
Total time taken = 240/x+520/y hr 240/x+520/y = 8+12/60 (12 minutes=12/60 hr)
240/x+520/y = 41/5 --------------- Equation 2
Multiply equation 1 by 3 and equation 2 by 2 and subtract equation 2 from equation 1
1800/y-1040/y = 24-82/5
760/y = 38/5
y = (760X5)/38
= 100
Putting y = 100 in equation 1
160/x+600/100 = 8
x = 80
Speed of Car = 100 km/hr
Speed of train = 80 km/hr