can you show me how to do this mathematically
A car traveling 90 km/h is 100 m behind a truck traveling 75 km/h. How long will it take the car to reach the truck?
Try this.
car|--0.100 km--|-------d---------|
t r u c k xxxxxx|-------d---------|
The truck travels a distance, d km, while the car travels d + 0.100 km.
distance = rate x time. The time must be equal so
time = distance/rate
time for truck = d/75
time for car = (d+0.100)/90
time = time
d/75 = (d+0.100)/90
solve for d and I get 0.5 km. So the truck travels 0.5 km and the car travels 0.6 km. How long does that take.
d = r*t
t = d/r
t = 0.5/75 = 0.00667 hr or
t = 0.6/90 = 0.00667 hr.
You can convert 0.00667 hr to minutes, then to sec by
0.00667 hr x (60 min/hr) x (60 sec/min) = I get 24 seconds but check my work.
There is another way to do this which is a little shorter.
Note that the difference between 90 km/hr and 75 km/hr is 15 km/hr. So we ask ourselves how long it takes to cover that additional 0.1 km at the rate of 15 km/hr. That is t=d/r = 0.100/15 = 0.00667 hr. Voila!
Thank You
24 seconds
To solve this problem mathematically, we can use the concept of relative velocity. The relative velocity between the car and the truck is the difference between their speeds. In this case, it is calculated as follows:
Relative velocity = Car's speed - Truck's speed
= 90 km/h - 75 km/h
= 15 km/h
Now, we know that the car is 100 meters behind the truck. To determine how long it will take for the car to reach the truck, we need to calculate the time it takes for the car to cover a distance of 100 meters (0.1 kilometers) at a speed of 15 km/h.
Time = Distance / Speed
= 0.1 km / 15 km/h
Calculating this division will give us the time required for the car to catch up to the truck.
Time = 0.1 km / 15 km/h
= 0.00667 hours
Since time is usually expressed in hours, we have our answer in hours. Therefore, it will take approximately 0.00667 hours (or about 24 seconds) for the car to reach the truck.