



 
Hi Sabrina, You have distance measured in metres and kilometres and time in hours and seconds. We need to decide on consistent units so I am going to measure distance in metres and time in seconds. There are 1,000 metres in a kilometre so 60 km/h is 60,000 m/h. There are 60 minutes in an hour and 60 seconds in a minute so there are 60 × 60 = 3,600 seconds on an hour. Thus 60,000 m/h is 60,000/3,600 m/s which simplifies to 100/6 m/s. Hence the train is travelling at 100/6 m/s. You can find the speed of the boat in metres per second. In my diagram P is the position of the train and Q the position of the boat when the train is directly over the boat. T is the position of the train and B the position of the boat t seconds later. The distance from P to Q is 20 metres. Since you know the speed of the train and the boat you can find the distance from P to T and the distance from Q to B, both of these are functions of time.. Triangle PQB is a right triangle so you can use Pythagoras theorem to find the distance from P to B. Triangle TPB is also a right triangle so you can again use use Pythagoras theorem to find the distance from T to B. I am going to call this distance f(t). Your problem is to find f '(10). I hope this helps,  


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