Hi ,this is a math problem, i don't think its really hard, but i still cant solve it. can anyone please help?

Question

A man on foot covers 25 km between two towns in 15/4 hours(3 and 3 quarter hours). He walks at 4km/hr for the first part of the journey and runs at 12km/hr for the remaining part.

a) How far did he run?

b) For how long was he running?

Please help all mathematicians. i'll give 10 points definitely.

Answer 1

Ok a) we will save until after we solve b

For b, you need to set up a basic algebraic relation.  Let x be the hours spent running.  3.75 - x will thus be the time spent walking (total time - time running).

Keep in mind that speed * time ~ distance:

25 km total = (walking speed * time spent walking) + (running speed * time spent running)

25km = 4km/hr * (3.75 - x) + 12km/hr * x

drop the units because this is math, not physics:

25 = 4(3.75-x)+12x

25 = 4*3.75 - 4x + 12x

25 - 4*3.75 = 8x

x = (25-4*3.75)/8 -> that's your answer for b

Then multiply that by the running speed to get the answer to part a:

12 * (25 - blah blah blah)

Remember to add units back in if your teacher is anal about stuff like that.