Problema Solution
Joan got on her bike and went for a ride. She rode at a speed of 16 miles per hour from her house to her sister's house, which is in another city along the way. The two women then got into a car and traveled at a speed of 50 miles per hour to their mother's house. The total distance from Joan's house to her mother's house (via her sister's house) is 315 miles, and Juan traveled for 8 hours. How far is it from Joan's house to her sister's house?
Answer provided by our tutors
v1 = 16 mph
d1 = the distance from Joans house to her sisters house
v2 = 50 mph
d2 = the distance from sister house to their mothers house
d1 + d2 = 315 total distance from Joan's house to her mother's house (via her sister's house) is 315 miles
t = 8 h
d1 = ?
since v = d/t => t = d/v
d1/16 + d2/50 = 8
by solving the system of equations
d1 + d2 = 315
d1/16 + d2/50 = 8
we find
d1 = 40 miles
d2 = 275 miles
click here to see the step by step solution of the system of equations
the distance from Joan's house to her sister's house is 40 miles.