Answer:
280 km
Step-by-step explanation:
Given that a bus, say
, leaves a station traveling north at speed of 70km/hour.
Half an hour later the second bus, say
, leaves a station traveling north at speed of 70km/hour.
As, distance = speed x time,
so, the distance traveled by bus
in 0.5 hours = 70 x 0.5 = 35 km.
Note that, both the buses are traveling in the same direction and when the second bus leaves the station, the first bus already covered a distance of 35 km.
Let the second bus took
hours to meet the first bus and both the buses meet at a distance of
km from the station.
The distance traveled by the first bus from the station,
km
![\Rightarroe t= \frac {d-35}{70}\cdots(i)](https://tex.z-dn.net/?f=%5CRightarroe%20t%3D%20%5Cfrac%20%7Bd-35%7D%7B70%7D%5Ccdots%28i%29)
and the distance traveled by the second bus,
km
![\Rightarrow t=\frac {d}{80}\cdots(ii)](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%5Cfrac%20%7Bd%7D%7B80%7D%5Ccdots%28ii%29)
Now, equation the equation (i) and (ii), we have
![\frac {d-35}{70}=\frac {d}{80} \\\\\Rightarrow 8(d-35)=7d \\\\\Rightarrow 8d - 280 = 7d \\\\\Rightarrow 8d-7d=280 \\\\\Rightarrow d = 280 km](https://tex.z-dn.net/?f=%5Cfrac%20%7Bd-35%7D%7B70%7D%3D%5Cfrac%20%7Bd%7D%7B80%7D%20%5C%5C%5C%5C%5CRightarrow%208%28d-35%29%3D7d%20%5C%5C%5C%5C%5CRightarrow%208d%20-%20280%20%3D%207d%20%5C%5C%5C%5C%5CRightarrow%208d-7d%3D280%20%5C%5C%5C%5C%5CRightarrow%20d%20%3D%20280%20km)
Hence, both the bus will meet at a distance of 280 km from the station.