Question 1101890
(Part (a) )


The speeds were given in {{{meters/second}}}, but the calculations should be better handled with kilometers, and hours.  The conversion factor to get KM per HOUR is {{{18/5}}}.



Both Kate and Ben traveled at {{{18+9(18/5)}}} kilom per hour for x hours; but first, Kate traveled at {{{5(18/5)}}} kilometers per hour for {{{1/2}}} hours.
Total distance given as 100 km.


x, time in hours while both were traveling toward each other                          
{{{highlight_green((18+9*18/5)x+18(1/2)=100)}}}


(omitting algebra steps here)


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

.






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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(meters/seconds)(1/1000)(kilometer/meters)(3600/1)(seconds/hour)}}}

{{{t*(1/1000)(3600)}}}

{{{t(3600/1000)}}}

{{{t(36/10)}}}

{{{t((2*18)/(2*5))}}}

{{{t*(18/5)}}}{{{kilometers/hour}}}


For a given {{{t}}} {{{m/seconds}}}, the same speed is {{{t(18/5)(kilometers/hour)}}}.