. How many hours did Daniel spend on the train on Friday?

Question

Last weekend Daniel traveled by train to visit his grandparents. On Friday he boarded an express train
that traveled at an average rate of 75 miles per hour. On Sunday he returned home on a slower train that
traveled at an average rate of 45 miles per hour. The total time Daniel spent on the trains last weekend
was 8 hours. How many hours did Daniel spend on the train on Friday?
[A] 3 hr [B] 8 hr [C] 2 hr [D] 5 hr

Answer 1

Hello William,

Let v = average rate, d = distance travelled, and t= time spent

v = d/t

 

v1= 75 mph

v2 = 45mph 

 

total time = t1 + t2  = 8

assume  d1 = d2

 

v1*t1 = v2*t2 

t2 = v1*t1/v2

 

Let's substitute t2 into the equation for total time:

t1 + (v1*t1/v2) = 8

t1[ 1 +v1/v2] = 8

t1 = 8/[1+(v1/v2) = 8/(1+75/45) = 3 hours