At 8.30 a.m., Tommy is driving from Town P to Town Q at a speed of 45 km/h while Jerry is driving from Town Q to Town P at 60 km/h. Town P and Town Q are 210 km apart. At what time will they meet?
To find the time they will meet, we need to determine the time it takes for each of them to travel to the meeting point.
Let's denote the time it takes for Tommy to reach the meeting point as T1, and the time it takes for Jerry to reach the same point as T2.
We know that Tommy's speed is 45 km/h and he starts driving at 8:30 a.m.
Therefore, the distance he covers by the time they meet is 45 * T1.
We also know that Jerry's speed is 60 km/h and he starts driving at 8:30 a.m.
Therefore, the distance he covers by the time they meet is 60 * T2.
Since they are traveling towards each other, the total distance they both cover is 210 km. Thus, we can write the equation:
45 * T1 + 60 * T2 = 210.
To solve for T1, we need to rewrite the equation using the same variable. We can rearrange the equation as follows:
45 * T1 = 210 - 60 * T2.
Now, let's express T1 in terms of T2:
T1 = (210 - 60 * T2) / 45.
To find the time they meet, we need to find the values of T1 and T2 that satisfy this equation.
First, let's see if they meet before or after 12:00 p.m.:
If they meet before 12:00 p.m., then T1 + 8:30 a.m. < 12:00 p.m., which means T1 < 3.5 hours.
If they meet after 12:00 p.m., then T1 + 8:30 a.m. > 12:00 p.m., which means T1 > 3.5 hours.
Now we can substitute T1 in terms of T2:
(210 - 60 * T2) / 45 < 3.5.
Let's solve this equation:
210 - 60 * T2 < 45 * 3.5,
210 - 60 * T2 < 157.5,
-60 * T2 < -52.5,
T2 > (-52.5) / -60,
T2 > 0.875.
Therefore, they meet after T2 > 0.875 hours.
Now let's find T1:
T1 = (210 - 60 * T2) / 45,
T1 = (210 - 60 * 0.875) / 45,
T1 = (210 - 52.5) / 45,
T1 = 157.5 / 45,
T1 = 3.5 hours.
Since T1 = 3.5 hours and they start driving at 8:30 a.m., they will meet at 8:30 a.m. + 3.5 hours = 12:00 p.m.
Therefore, they will meet at 12:00 p.m.
What a ridiculous solution by the bot for such a very easy question and then to reach the wrong answer !!!
Of course when they meet, they both have gone the same time !
and the total distance covered would be 210 km
Le the time be t hours
45t + 60t = 210
t = 210/105 hrs = 2 hours
So if they both left at 8:30 am, they would meet at 10:00 am
Apologies for the confusion in the previous response. You are absolutely correct. When they meet, they will both have traveled for the same amount of time. The total distance covered would be 210 km, and the equation 45t + 60t = 210 can be used to find the time. Solving this equation, we find t = 2 hours. Therefore, they will meet at 8:30 am + 2 hours = 10:30 am. Thank you for pointing out the mistake, and I apologize for any confusion caused.
To find the time they will meet, we need to determine how long it will take each of them to cover the distance between the towns.
Let's start with Tommy:
Tommy is driving at a speed of 45 km/h and needs to cover a distance of 210 km. We can use the formula: Time = Distance/Speed.
So, Tommy's time is 210 km / 45 km/h = 4.67 hours (rounded to two decimal places).
Now, let's calculate Jerry's time:
Jerry is driving at a speed of 60 km/h and also needs to cover a distance of 210 km.
Jerry's time is 210 km / 60 km/h = 3.50 hours.
Since they are both driving towards each other, we can add their times together to find the total time it will take for them to meet:
Total time = Tommy's time + Jerry's time = 4.67 hours + 3.50 hours = 8.17 hours (rounded to two decimal places).
To determine the meeting time, we need to add this total time to the starting time of 8:30 a.m.:
8:30 a.m. + 8.17 hours = 4:47 p.m.
Therefore, Tommy and Jerry will meet at approximately 4:47 p.m.