# Math Problem. How long is the Troop? In the last December coup attempt, a troop soldiers march 6 km going to Fort Bonifacio from Makati, after they agreed to go back to barracks. at the same time, the General supervising the march rode from the rear of the troop to the front and back at once to the rear. If the distance covered by the general is 10 km and both the troop and the general traveled a uniform rate. How long is the troop? A detail solution please. Thank you.

1
by VilesX

2014-06-10T03:27:18+08:00
Assume that the time to reach the barracks = 1 hr:
General = 10km/hr
troop = 6km/hr

Assume that the general is going from barracks to makati:
Get the intersection of the general and the troup:
6km = r1t1 + r2t2
since t1 = t2
6km = 10km/hr (t) + 6km/hr (t)
t = 3/8hr

get the distance travelled by the general after 3/8 hr:
3/8hr * 10km/hr = 15/4km

get the distance travelled by the troop after 3/8 hr:
3/8hr * 6km/hr = 9/4km

it would be like this:

<-------------------------6km----------------------------------------------->
<---troop=9/4km--><------------general=15/4km---------------->

get the time for the general to reach makati:
(9/4km) / (10km/hr) = 9/40 hr

get the time remaining after he arrive at makati:
9/40hr + 3/8hr + x = 1
x = 3/5

multiply the time remaining to the rate of the general and divide it by two since it is equal to length of the troop:
3/5hr * 10km/hr = 6km/2 = 3km