Problem22: To get to the camp in time, tourists had to go with a speed 4km/h. They went with that speed half of the road, but then they drove with a bus and arrived to the camp 2h 20min before the planned time. How many kilometers did tourists drive with the bus, if the speed of the bus was 60km/h?
This problem can be solved using distance formula;
\[ s=vt \]
Here we suppose;
Speed of Tourists=v1=4 km/h
speed of bus=v2=60km/h
Total time to be taken by the tourists to reach the camp without bus=t
Time taken by tourists when bus used=t-2h20min=t-140min
let the total distance is ‘x’ but half is travelled without bus and other half by bus!
for first half distance=s1 =x/2
for second half distance=s2=x/2
Using s=vt formula for first half;
\[ \frac{x}{2}=4\times t \]—1
for second half using same formula;
\[ \frac{x}{2}=60\times (t-140) \]—-2
bothe above equations are showing equal distances so,
\[ 4\times t=60\times (t-140) \]
we get after simplification,
\[ 56t=8400 \]
so,
\[ t= 150 min \]
dividing by 60 to get in hours;
\[ t=2.5 hours \]
put this value of ‘t’ in any of the above equations , say we put in (1)
we get;
\[ \frac{x}{2}=4 \times2.5 \]
we get,
\[ x= 20 km \]
So they travelled with the bus 20 kilometers