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Question-1

It took cindy 2 hours to bike from Abbott to Benson at a constant speed. The return trip took only 1.5 hours because she increased her speed by 6 km/h. how far apart are the two cities?

 

Let Cindy's speed to Benson =S

Her return speed =S+6

 

2S = 1.5(S+6), solve for S

S = 18 km/h - Cindy's speed to Benson.

18 x 2 =36 km - the distance between the two cities.

 

Question-2 

George takes a round-trip flight. On his departing flight his plane goes against the wind and only averages 450mph. On his return flight, his flight averages 550mph. If the total time George is on the plane while it is traveling is 6 hours, how much time does his return flight home take?

 

Let the departing time = t

The return time =6 - t

 

450t =550(6 - t), solve for t

t = 3.3 Hours it took on his departing trip.

6 - 3.3 = 2.7 hours, or 2 hours and 42 minutes took on his return trip.

 

 

Question-3

Two planes leave from the same location. The slower plane leaves first at 10:00 am. An hour later, the faster plane leaves, flying 150 mph faster. If the faster plane catches up to the slower one at 2:00 pm, what is the distance  both planes have traveled by 2:00 pm.

 

Let the speed of slower plane = S

The speed of the faster plane =S + 150

 

4S = 3(S +150), solve for S

S = 450 Miles - the speed of the slower plane

450 + 150 =600 Miles - the speed of the faster planes

4 x 450 = 3 x 600 =1,800 Miles - the distance travelled by both planes.

 

Question- 4

Betty leaves her house traveling 45 mph to a family reunion. An hour later, her stster leaves travelling 60 mph, along the same route. How long before Betty's sister catches up to her?

 

Since the LCM of 45 and 60 is 180 miles, it therefore follows that:

180 / 45 =4 hours since Betty left her house

180/60 =3 hours when her sister caught up with Betty.