Question

Fred and Sara meet at a lake to race their boats. The boats start at one end of the lake and travel 126 m straight across the lake and then return to where they started. Fred's boat goes across with an average speed 57.5 km/h and returns with that same average speed of 57.5 km/h. Sara's boat travels with an average speed of 31.1 km/h across the lake and then travels with an average speed of 88.8 km/h on the return trip.
a. Determine who wins the race and by how much time (in seconds) they win the race.
b. How much distance is between the boats when the winner crosses (neglect any accelerations and assume constant speeds)?

Answer 1

Ans: The length of the race is d=d1+d2= 126+126= 252m

For fred: Average speeds for first half of the length=v1=57.5km/hr=15.97 m/s=v2

Time taken for one side =t1=d1/v1= 7.89 s

Similarly for other side =t2=d2/v2 =7.89 s

Total time taken by fred to complete t=t1+t2= 15.78 s

For Sara: Average speed for one side v1=31.1 km/hr=8.64 m/s

Time taken t1=d1/v1= 14.58 s

Average speed for other side v2= 88.8 km/hr= 24.67 m/s

Time take t2=b d2/v2=5.11 s

Total time taken by Sara to complete= t1+t2=19.69 s

a) Sara taken more time than Fred therefore Fred will win the race by 19.69-15.78=3.91 s

b) For 14.58s Sara completed half of the length and she moves with average velocity 88.8km/hr=24.67 m/s for 15.78-14.58=1.2s. And the distance moved is 24.67*1.2= 29.60 m

Therefore the distance between Fred and Sara when race finished is 126-29.60=96.40 m