Fatima leaves her house to go to her friend Nabil’s place. Her speed is 4.5km/h. When she returns home, her speed is slower, 3.5km/h. Her total walking time to get to Nabil’s and back was 40 minutes. - how long does it take Fatima to get to Nabil’s house?
Q. Fatima leaves her house to go to her friend Nabil’s place. Her speed is 4.5km/h. When she returns home, her speed is slower, 3.5km/h. Her total walking time to get to Nabil’s and back was 40 minutes. - how long does it take Fatima to get to Nabil’s house?
Convert to Hours: First, let's convert the total walking time from minutes to hours, since the speeds are given in km/h.Total walking time in hours = 40 minutes ÷60 minutes/hourTotal walking time in hours = 32 hours
Distance and Time Formula: Let's denote the distance from Fatima's house to Nabil's place as Dkm. We can use the formula time=speeddistance to express the time it takes for Fatima to travel to Nabil's house and back.Time to Nabil's house = 4.5km/hDTime to return home = 3.5km/hD
Total Walking Time Equation: The total time spent walking is the sum of the time to get to Nabil's house and the time to return home.Total walking time = Time to Nabil's house + Time to return home32 hours = 4.5D km/h + 3.5D km/h
Combine Fractions: Now we need to solve for D. To do this, we can find a common denominator for the two fractions and combine them into a single equation.32 hours = 4.5×3.5D×3.5+D×4.5
Clear Fractions: Multiply both sides of the equation by the common denominator (4.5×3.5) to clear the fractions.(32)×(4.5×3.5)=D×3.5+D×4.5
Multiply Left Side: Perform the multiplication on the left side of the equation.(32)×(4.5×3.5)=2×(4.5×3.5)/3(32)×(4.5×3.5)=2×15.75/3(32)×(4.5×3.5)=31.5/3(32)×(4.5×3.5)=10.5
Distribute D: Now distribute D on the right side of the equation.10.5=D×(3.5+4.5)10.5=D×8
Solve for D: Divide both sides by 8 to solve for D.D=810.5D=1.3125 km
Find Time to Nabil's House: Now that we have the distance D, we can find the time it took Fatima to get to Nabil's house using her speed of 4.5 km/h.Time to Nabil's house = D/4.5 km/hTime to Nabil's house = 1.3125 km / 4.5 km/h
Divide to Find Time: Perform the division to find the time.Time to Nabil's house = 4.51.3125Time to Nabil's house = 0.291666… hours
Convert to Minutes: Finally, convert the time back to minutes, since the question prompt asks for the time in minutes.Time to Nabil's house in minutes = 0.291666… hours ×60 minutes/hourTime to Nabil's house in minutes = 17.5 minutes
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