SOLUTION: Hi A person covers 2/3 of his journey at his usual speed and the remaining distance at 3/4 of the usual speed and takes 30min more than the usual time. If total distance is 180

Question 1154666: Hi
A person covers 2/3 of his journey at his usual speed and the remaining distance at 3/4 of the usual speed and takes 30min more than the usual time. If total distance is 180km what is the usual speed.
Thanks
Found 3 solutions by mananth, math_helper, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

A person covers 2/3 of his journey at his usual speed and the remaining distance at 3/4 of the usual speed and takes 30min more than the usual time. If total distance is 180km what is the usual speed.
2/3 * 180 =120

let the usual speed be x km/h
distance 120 km
time = 120/x First part
distance = 60 km
speed = 3x/4
Time taken = 60/(3x/4)
=240/3x
=80/x II part
120/x +80/x = 180/x + 1/2 ( 30 minutes =1/2)
200/x = 180/x +1/2
20/x = 1/2
x= 40 km/h

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

Make use of distance = rate * time:
d = r*t
where we solve for t:
t = d/r

Notation
= usual speed
= usual time
(1) (time in hours)
So far, one equation with two unknowns. We find the 2nd equation by noting equation for the usual speed:
(2)
From here, substitute the LHS of (2) into the RHS of (1) and solve to get:

Check:
180km/(40km/hr) = 4.5hrs (the usual time)
(2/3)(180)/40 + (1/3)(180)/((3/4)40) = 3hrs + 2hrs = 5hrs (1/2hr longer than the usual time, so this is ok)

Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.

            I'd like to contribute my 2 cents to this problem's solution.

It is clear that we can exclude the first 2/3 of the journey from the consideration, since at this part there is no delay comparing with the standard schedule. The difference arises on the remained 1/3 distance, which is 60 miles. For this part of 60 miles, we have a regular time , where x is the regular speed. With the speed of , the spent time is = . So, the delay equation is - = (which is half of an hour) From the equation, = ; hence, x = = 2*20 = 40 kilometers per hour. ANSWER

Solved.

I hope that my setup is simpler and, therefore, more attractive.

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