Pete and jan compete as a team in a biathlon. Pete runs at a speed of 9 km/ h for x hours. Jan cycles at twice Pete's running speed for 1 hour and 30 minutes. The total distance of the biathlon is 42 km. Find, in hour and minutes, Pete's running time.
Distance = Rate * Time or D = RT
for Pete : D = 9x
for Jan : D = 18(1.5)
so 9x + 18(1.5) = 42
solve for x
(I got 1 hour, 40 minutes)
To find Pete's running time, let's first convert Jan's cycling time to hours.
Jan cycles for 1 hour and 30 minutes, which can be written as 1.5 hours (since 30 minutes is half an hour).
Now, let's determine the distances covered by both Pete and Jan.
Pete's distance = Pete's speed * Pete's running time
Jan's distance = Jan's speed * Jan's cycling time
We know that Pete's running speed is 9 km/h. Therefore, Pete's distance is 9 km/h * x hours = 9x km.
Jan's cycling speed is twice Pete's running speed, which means Jan's speed is 2 * 9 km/h = 18 km/h. Therefore, Jan's distance is 18 km/h * 1.5 hours = 27 km.
The total distance of the biathlon is 42 km. This means Pete's distance + Jan's distance = 42 km.
Substituting the values, we have:
9x km + 27 km = 42 km.
Combining like terms:
9x + 27 = 42.
Next, we can solve for x:
9x = 42 - 27,
9x = 15,
x = 15 / 9,
x ≈ 1.67 hours.
Finally, we need to convert x to hours and minutes:
1.67 hours = 1 hour and (0.67 * 60) minutes.
Calculating the minutes:
1 hour and (0.67 * 60) minutes = 1 hour and 40.2 minutes.
Therefore, Pete's running time is approximately 1 hour and 40.2 minutes.