Question 1173083: During the COVID 19 pandemic, Jerry, a front liner nurse, decided to use his bicycle since it was difficult for him to ride jeepneys in going to his work station. If he biked 5kilometers from his house to the hospital at a rate of x kph. For his return trip in going home, his rate was 1kph faster. It took him 2.5hours for the entire round trip. Find his rate and time in going to the hospital.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! speed*time=distance
x *y=5, where x is speed in km/h and y is time in hours
on way back it ix (x+1)*(2.5-y)=5
since the two equations are equal to 5, they are equal to each other
so xy=2.5x-xy+2.5-y or 5=2.5x-5+2.5-y, or 7.5=2.5x-y
x=(5/y)
so 7.5=2.5*(5/y)-y
7.5=(12.5/y)-y
y^2+7.5y-12.5=0
or 2y^2+15y-25=0
y=(1/4)(-15+/- sqrt(225+200)) sqrt(425)=20.62
so y=5.62/4=1.405 hr.only positive root
x=3.559 km/h for 1.405 hr. This is the answer,
on way back it was 4.559 km/h for 1.096 hr.
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