Train X leaves Dhaka at 10:00 AM and travels East at a constant speed of x miles per hour . If another Train Y leaves Dhaka at 11:30 AM and travels east along the same tracks at speed 4x/3 , then at what time will Train Y catch Train X ?

Question

নিচের অপশন গুলা দেখুন

• 4 PM same day
• None of them
• 1 PM same day
• 6 PM same day

Answer 1

সঠিক উত্তর হচ্ছে: op4 PM same day

ব্যাখ্যা:

For rate-time-distance questions, try to reduce the question to as few unknown quantities as possible. Instead of a separate r, t, and d for each train, look for commonalities:
Both trains travel the same distance, so there's only one "d"
We don't know the time, but we know that Train Y took less time, since it left an hour and half later. So if Train X took t hours to travel some distance, Train Y only took (t-1.5) hours.
The rates aren't given, but we know that train Y was 4/3 the rate of train X.
Let's set it up. Since rate*time= distance and the distances are equal, we can set Train X's rate * time equal to Train Y's rate * time
xt=43x(t−1.5)xt=43x(t−1.5)
Working through the problem, we get
xt=43xt−4/3∗1.5xt=43xt−4/3∗1.5 here it can be helpful to recognize that 1.5 is just 3232, and cancel out the 3's: 43∗32=243∗32=2
xt=43xt−2xt=43xt−2
Subtract xt from both sides, and add 2 to both sides, and we get: 2=13t2=(1/3)t
6 = t
So, adding 6 hours to Train X's starting time, we get 4:00 pm as the time that train Y will catch train X.