Math word problem

Question

A cyclist rode 96 km 2 hours faster than planned, because every hour he rode 1 km more than planned in 1 h 15 min. Find the velocity of the cyclist.

Answer 1

d = r(t)

So,

96 = (the expected speed)(the expected time)

But, they went faster than expected. They finished 2 hours earlier, so the new time is the old time -2.

I'm not sure if you meant his speed was 1km/h faster or if he went 1 km further every 1h15min.

If the former, then we can say his new rate is equal to his old rate +1.

So, 96 = (r + 1)(t - 2)

We can also solve the original d=rt for t

t = 96/r

Now we can substitute that in

96 = (r + 1)(96/r - 2)

At this point, you can throw this into a graphing calculator to find the original speed was approximately 6.4 kph (4 mph)

And the new rate about 7.4 kph. (4.6mph)

Plug that in to find the original time, approximately 14.9 hours (14 hrs 54 min)

Thus the new time is about 12.9 hours

Answer 2

He started at 47.5kph then got to 48.5;

avg=48 so *1.25=60kph.