Problema Solution
A man goes out at 16:42 and arrives at a post box 6km away, at 17:30. He walked part of the way at 5km/h and then, realising the time, he ran the rest of the way at 10km/h. How far did he have to run?
Answer provided by our tutors
The total time of the travel is: 48 min = 48/60 hr = 4/5 hr
v1 = 5 km/h
t1 = the time of the part that the man walked with v1 = 5 km/h
v2 = 10 km/h
t2 = the time of the part that the man ran with v1 = 10 km/h
t1 + t2 = 4/5
Since speed*time = distance we can write:
v1t1 + v2t2 = 6
5t1 + 10t2 = 6
Now we have the following system of equations:
t1 + t2 = 4/5
5t1 + 10t2 = 6
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click here to see the system of equations solved for t1 and t2
........
t1 = 2/5 hr
t2 = 2/5 hr
The distance that the man ran was v1t1 = 5*(2/5) = 2 km.