Ivan and kate live 40 miles apart. ivan leaves his house at 8: 00
a. m. and bicycles towards kate's house at a constant speed of 12 mph. kate leaves her house at 9: 30
a. m. bicycles towards ivan at constant speed of 16 mph. at what time will they meet?

Time at which the meet = 10:17:24 am

Step-by-step explanation:

Speed of Ivan = 12 mph

Speed of Kate = 16 mph

Total distance traveled = Initial separation = 40 miles

Ivan leaves his house at 8:00  a.m and Kate leaves her house at 9:30  a.m

If t is the time of catch up after Ivan starting, time taken by Kate is t - 1.5,

We have

             Distance = Speed x Time

          Total distance traveled = Distance traveled by Kate + Distance traveled by Ivan

        40 = t x 12 + (t-1.5) x 16

         40 = 28t - 24

          28t = 64

              t = 2.29 hours

So after 2.29 hours of Ivan's starting they meet,

Time = 8:00 am + 2.29 hours = 10:00 am + 0.29 x 60 minutes = 10:17am + 0.4 x 60 seconds = 10:17:24 am

Time at which the meet = 10:17:24 am

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