Cyclist starts a journey at 10:30 am and plans to get home 45km away by 3:00pm at first he travels for 2hour at 71/2 km/h and xkm/h for the rest of the time in order to arrive promptly at home .find the value of x
7.5 km/hr * 2 hr = 15 km (not 35.5)
45 km - 15 km = 30 km still to ride
It is now 12:30 pm so to get home by 3 pm he must go 30 km in 2.5 hours
30 km / 2.5 hr = 12 km/hr
Let's start by finding out how far the cyclist travels in the first 2 hours:
Distance = Speed x Time
Distance = (71/2) km/h x 2 h
Distance = 71/2 x 2
Distance = 71/2 x 2/1
Distance = 71/1
Distance = 35.5 km
So the cyclist has 45 km - 35.5 km = 9.5 km left to travel.
Let's call the time the cyclist travels at x km/h "t" (in hours). We know that the total journey time is 4.5 hours (from 10:30 am to 3:00 pm), so:
2 + t = 4.5
Solving for t, we get:
t = 4.5 - 2
t = 2.5 hours
Now we can use the formula Distance = Speed x Time again to find x:
Distance = Speed x Time
9.5 km = x km/h x 2.5 h
9.5 km / 2.5 h = x km/h
x = 3.8 km/h
Therefore, the cyclist needs to travel at a speed of 3.8 km/h for the remaining 2.5 hours in order to arrive home by 3:00 pm.