At 10:00 AM a truck started traveling from point A with a speed of 40mph. 3 hours and 10 minutes later a car started to drive from point A in the same direction with an average speed of 60mph. At what time will the car catch up with the truck?
To find out at what time the car will catch up with the truck, we need to determine the distance traveled by both vehicles and their relative speeds.
Step 1: Convert 3 hours and 10 minutes to hours.
10 minutes is equal to 10/60 = 1/6 hours.
So, 3 hours and 10 minutes is equivalent to 3 + 1/6 = 19/6 hours.
Step 2: Determine the distance covered by the truck in the time it took for the car to start.
Distance = Speed × Time
Distance covered by the truck = 40 mph × 19/6 hours
Distance covered by the truck = 760/6 miles
Distance covered by the truck = 126 2/3 miles
Step 3: Set up the equation for the time it takes for the car to catch up with the truck.
Let t be the time (in hours) it takes for the car to catch up with the truck. At this time, both the truck and the car will have traveled the same distance.
Distance covered by the truck = Distance covered by the car
126 2/3 miles = 60 mph × t
Step 4: Solve for t.
t = (126 2/3 miles) / 60 mph
t = (380/3) / 60 hours
t ≈ 2.11 hours
Step 5: Add the time it took for the car to start to the time t to get the total time it took for the car to catch up.
Total time = (19/6) + 2.11
Total time ≈ 3.44 hours
Step 6: Determine the time at which the car caught up with the truck.
10:00 AM + 3.44 hours ≈ 1:26 PM
Therefore, the car will catch up with the truck at approximately 1:26 PM.
To find the time when the car catches up with the truck, we need to calculate the time it takes for the car to cover the same distance as the truck.
First, let's convert the 3 hours and 10 minutes into hours. There are 60 minutes in an hour, so the 10 minutes is equal to 10/60 = 1/6 hour. Therefore, the truck has a head start of 3 + 1/6 = 19/6 hours.
Now, let's find the distance traveled by the truck during this time. The distance is equal to the speed multiplied by the time: distance_truck = speed_truck * time_truck = 40 mph * (19/6) hours = 760/6 miles.
Since the car is traveling at a speed of 60 mph, we can find the time needed to cover the same distance as the truck: time_car = distance_truck / speed_car = (760/6) miles / 60 mph = (760/6) / 60 hours.
To simplify the calculation, let's convert 760/6 to a decimal: (760/6) / 60 = 126.67 / 60 = 2.111 hours.
Now, we add this time to the starting time of the truck to find the time when the car catches up with the truck. The starting time of the truck is 10:00 AM, so we add 2.111 hours to 10:00 AM.
10:00 AM + 2.111 hours = 12:06 PM.
Therefore, the car will catch up with the truck at 12:06 PM.
At the catch-up point, they will have travelled the same distance.
Time taken by car ---- x hrs
time taken by truck ---- x + 19/6 hrs (which is 3 hrs, 10 min)
60x = 40(x+19/6)
60x = 40x + 380/3
20x = 380/3
x = 19/3 hrs or 6 hrs, and 20 minutes
Interpret my answer .
Truck: d1 = 40mi/h * 3.1667h = 126.67 mi. head-start.
126.67 + 40 * T = 60 * T.
20T = 126.67,
T = 6.33h = 6hrs, and 20 min.