James and Jack are driving at 80 km/h and 60 km/h respectively. Every hour, James increases his speed by 3 km/h. Find their speed difference after 5 hours. Please explain method clearly. What I am confused with is, for the first hour do you start with 80 km/h speed and 60 km/h speed or do you start with 82 km/h and 57 km/h. In what types of questions would you start with the first and in what question would you start with the second pair of speeds. Another question is: John is driving at a speed of 50 km/h. If he increases hispeed by 20% every hour, then how many km can he cover in 3 hours? This question is using the original speed 50km/h as the speed for the first hour. Please help... really stuck...
james speed: Vj=80+3t where t is hours elapsed.
speed difference= vj-60=20+3t after three hours, =20+15
Second question:
distance=speed*time= (50(1+1.2+1.2^2) = 182km
Pls explain clearly
To find the speed difference between James and Jack after 5 hours, let's break it down step by step.
Step 1: Determine the speeds of James and Jack after each hour.
James starts at 80 km/h and increases his speed by 3 km/h every hour. So, his speeds after each hour are:
Hour 1: 80 km/h
Hour 2: 83 km/h
Hour 3: 86 km/h
Hour 4: 89 km/h
Hour 5: 92 km/h
Jack drives at a constant speed of 60 km/h, so his speed remains the same throughout the time.
Step 2: Calculate the speed difference between James and Jack after 5 hours.
After 5 hours, James is driving at 92 km/h, and Jack is driving at 60 km/h. The speed difference is obtained by subtracting Jack's speed from James's speed:
Speed Difference = James's speed - Jack's speed
Speed Difference = 92 km/h - 60 km/h
Speed Difference = 32 km/h
Therefore, after 5 hours, James and Jack will have a speed difference of 32 km/h.
Now, let's address your confusion about starting speeds.
In the first example, we started with James's speed at 80 km/h and then calculated the speeds after each hour by increasing it by 3 km/h. For Jack, we assumed a constant speed of 60 km/h because the problem didn't provide any information about changes in his speed.
In the second example, John starts with a speed of 50 km/h. The problem states that he increases his speed by 20% every hour. Hence, we use the original speed of 50 km/h for the first hour, and then increase it by 20% for subsequent hours.
Let's calculate the distance John can cover in 3 hours.
Step 1: Calculate John's speed after each hour.
Hour 1: 50 km/h
Hour 2: 50 km/h + (20% of 50 km/h) = 50 km/h + 10 km/h = 60 km/h
Hour 3: 60 km/h + (20% of 60 km/h) = 60 km/h + 12 km/h = 72 km/h
Step 2: Calculate the total distance covered by John in 3 hours.
To find the distance covered, we need to multiply John's speed by the time he spends driving:
Distance = Speed × Time
Distance for Hour 1 = 50 km/h × 1 hour = 50 km
Distance for Hour 2 = 60 km/h × 1 hour = 60 km
Distance for Hour 3 = 72 km/h × 1 hour = 72 km
Total distance covered in 3 hours = Distance Hour 1 + Distance Hour 2 + Distance Hour 3
Total distance covered in 3 hours = 50 km + 60 km + 72 km
Total distance covered in 3 hours = 182 km
Therefore, John can cover a distance of 182 km in 3 hours.