Given a distance, two different speeds and time how to determine how far was traveled on each speed.

Question

For example, if 100m has been traveled in 5 seconds and there was the option to travel the distance by bike and on foot. Speed on bike is 40m/s and speed on foot is 10m/s, how far did the person travel by bike and how much on foot? (Yes values are not actual representation of the real world)

score 0 · Accepted Answer · answered Sep 27 '13 at 07:49

0

traveled distance=D=100

time taken=t=10

t=time on foot+time on bike=tf+tb

D=10*time on foot+40*time on bike=10tf+40tb

100=10tf+40tb => tf=10-4tb

edit: time taken was actually 5, not 10, but the idea is the same

answered Sep 27 '13 at 07:49

user2520938

7,235

I got this far as well, but the problem is tf nor tb is known – user1435395 Sep 27 '13 at 08:01
Well tf+tb=5, tf=10-4tb. substituting: 10-4tb+tb=5 -> -3tb=-5 ->tb=5/3 -> tf=10-4*(5/3)=1/3 – user2520938 Sep 27 '13 at 08:06
Totally forgot about the substitution, let's just say it was still early – user1435395 Sep 27 '13 at 08:28

score 0 · Answer 2 · answered Sep 27 '13 at 07:52

0

Let $t_1$ denote the time travelled on foot and $t_2$ the time travelled by bike. Then we have on one side $$ t_1 + t_2 = 5$$ on the other hand, if we consider the travelled distance $$ 10t_1 + 40t_2 = 100. $$ Can you do it from here?

answered Sep 27 '13 at 07:52

martini

84,101

I got this far as well, but the problem is t1 nor t2 is known – user1435395 Sep 27 '13 at 08:00

score 0 · Answer 3 · answered Sep 27 '13 at 08:05

0

You say that you've gotten to the point where you have two equations and two variables - so what's the problem? Do you need help with the algebra? Solve for t1 in one equation in terms of t2, then substitute that in the second equation to solve for t2.

answered Sep 27 '13 at 08:05

Red Alert

101

Totally forgot about the substitution, let's just say it was still early – user1435395 Sep 27 '13 at 08:29

Given a distance, two different speeds and time how to determine how far was traveled on each speed.

3 Answers3