SOLUTION: Kate leaves town P and cycles towards town Q which is 100 km away, at the speed of 5 metres/ second. Thirty minutes later, Ben leaves town Q and travels towards town P at 9 metres/

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Kate leaves town P and cycles towards town Q which is 100 km away, at the speed of 5 metres/ second. Thirty minutes later, Ben leaves town Q and travels towards town P at 9 metres/      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1101890: Kate leaves town P and cycles towards town Q which is 100 km away, at the speed of 5 metres/ second. Thirty minutes later, Ben leaves town Q and travels towards town P at 9 metres/second.
a. How long has Ben been traveling for when he meets Kate?
b. How many kilometres from P are they when they meet?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(Part (a) )

The speeds were given in meters%2Fsecond, but the calculations should be better handled with kilometers, and hours. The conversion factor to get KM per HOUR is 18%2F5.


Both Kate and Ben traveled at 18%2B9%2818%2F5%29 kilom per hour for x hours; but first, Kate traveled at 5%2818%2F5%29 kilometers per hour for 1%2F2 hours.
Total distance given as 100 km.

x, time in hours while both were traveling toward each other
highlight_green%28%2818%2B9%2A18%2F5%29x%2B18%281%2F2%29=100%29

(omitting algebra steps here)

x=1.806hours
1 hour 48 minutes
Time for Ben to meet Kate between P and Q.
.





----------------
The speed unit conversions:
1 hour is 3600 seconds.
1 kilometer is 1000 meters.
Problem description gave speeds in meters per second but gave distance in kilometers and problem may be more easily handled in KILOMETERS, HOURS.

Any given t meters per seconds, as speed

t%2A%281%2F1000%29%283600%29
t%283600%2F1000%29
t%2836%2F10%29
t%28%282%2A18%29%2F%282%2A5%29%29
t%2A%2818%2F5%29kilometers%2Fhour

For a given t m%2Fseconds, the same speed is t%2818%2F5%29%28kilometers%2Fhour%29.