Question: A Toyota car travelled at the rate of 70 km/hour leaves the house 2 hours after a Kia car has left and overtakes it in 5 hours. at what rate was Kia car travelling?
distance = 70 * 5 = 350 km
speed = distance / time
= 350 / (5 + 2)
Well, well, looks like our Toyota car was just a little late for the party! Let's do some math here. If the Toyota car overtakes the Kia car in 5 hours and the Toyota car traveled at 70 km/h, we know that the Kia car had a head start of 5 hours. So, if we subtract those 5 hours from the total time the Toyota car traveled, we will find out how long the Kia car was on the road. You followin' me?
Now, since the Kia car started 2 hours earlier than the Toyota car, and then traveled for some unknown time, let's call it "x" hours. Therefore, the total time the Toyota car traveled is "x + 5" hours. Easy, right?
Now, we know that the distance traveled by both cars is the same when the Toyota overtakes the Kia. So... wait for it... distance equals rate multiplied by time! In other words, the distance covered by the Toyota car is 70 km/h multiplied by (x + 5) hours, and the distance covered by the Kia car is... Yeah, you guessed it... x hours multiplied by its rate. Still following along?
Since the distances are equal, we can set up an equation. 70 km/h multiplied by (x + 5) hours is equal to x hours multiplied by... the Kia car's rate! Yeah, we finally got there. So, let's solve that equation and find out the rate at which the Kia car was traveling. Trust me, it will be worth the wait!
Step 1: Let's denote the rate of the Kia car as 'x' km/hour.
Step 2: The Toyota car left 2 hours later than the Kia car and traveled the same distance in 5 hours.
Step 3: Since speed = distance/time, we can calculate the distance traveled by the Toyota car as 70 km/hour × 5 hours = 350 km.
Step 4: The Kia car also traveled the same distance in 7 hours (5 hours from the Toyota car's travel time + 2 hours delay).
Step 5: Using the formula distance = speed × time, we can set up the equation: distance traveled by the Kia car = x km/hour × 7 hours = 350 km.
Step 6: Solving for x, we divide both sides of the equation by 7 hours:
x km/hour = 350 km ÷ 7 hours.
Step 7: Simplifying, we find:
x km/hour = 50 km/hour.
Step 8: Therefore, the Kia car was traveling at a rate of 50 km/hour.
To find the rate at which the Kia car was traveling, we need to use the concept of relative motion. Let's break down the information given in the question to solve it step by step:
1. The Toyota car was traveling at a constant speed of 70 km/hour.
2. The Toyota car started 2 hours after the Kia car.
3. The Toyota car overtakes the Kia car after 5 hours.
We can represent the distance covered by each car using the formula: Distance = Speed × Time.
For the Toyota car:
Distance covered by the Toyota car = 70 km/hour × (Time + 2 hours)
For the Kia car:
Distance covered by the Kia car = Speed of the Kia car × Time
Since the Toyota car overtakes the Kia car at some point, their distances are equal when the overtaking occurs. Therefore, we have the equation:
70 km/hour × (Time + 2 hours) = Speed of the Kia car × 5 hours
Now, we can solve for the speed of the Kia car by rearranging the equation. Divide both sides of the equation by 5:
70 km/hour × (Time + 2 hours) / 5 = Speed of the Kia car
Simplifying the equation further:
14 km/hour × (Time + 2 hours) = Speed of the Kia car
So, the speed of the Kia car is 14 km/hour multiplied by the time it took for the Toyota car to overtake it plus the 2-hour head start.
Note: To find the exact speed of the Kia car, we would need to know the specific value of time.