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

Question

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 travelling for when he meets Kate? b. How many kilometres from P are they when they meet

Answer 1

Let x = number of minutes traveled by Kate when they meet

 

Then x - 30 = number of minutes traveled by Ben when they meet

 

Kate's speed = 5 m/sec = (5 m/sec)(60 sec/min)(1 km/1000 m) = 0.3 km/min

Ben's speed = 9 m/sec = (9 m/sec)(60 sec/min)(1 km/1000 m) = 0.54 km/min

 

Distance = (Rate)(Time)

 

When they meet, (Distance of Kate) + (Distance of Ben) = 100

 

So, 0.3x + 0.54(x-30) = 100

 

      0.3x + 0.54x - 16.2 = 100

 

                           0.84x = 116.2      x = 138.33333 min

 

a. Time traveled by Ben when they meet = x-30 = 108.33333 min = 108 min 20 sec

 

b. Distance from P when they meet = 0.3x = (0.3 km/min)(138.33333 min) = 41.5 km