A girl cycles from her house to a friend’s house at 22 km/h and home again at 26 km/h. If the
round trip takes 54 min, how far is it to her friend’s house?
Round your answer to the nearest 0.1 km.
[
22 + 26 = 48
48/2 = 24 km/h
54 / 24 = 2.25 = 2.3 km
This solution had minutes divided by kilometers per hour. Resulting in units of minute hours / kilometers. There is no use of similar units.
To find the distance to her friend's house, we'll need to use the formula:
Distance = Speed x Time
Let's denote the distance from her house to her friend's house as "d" km.
The time it takes for the girl to cycle from her house to her friend's house is given as:
Time1 = d / 22 (since the speed is 22 km/h)
The time it takes for the girl to cycle from her friend's house back to her own house is given as:
Time2 = d / 26 (since the speed is 26 km/h)
We know that the round trip takes a total of 54 minutes, which can be expressed as 0.9 hours (since there are 60 minutes in an hour).
So we have the equation:
Time1 + Time2 = 0.9
Substituting the values of Time1 and Time2:
(d / 22) + (d / 26) = 0.9
To solve this equation, we can multiply both sides by the least common multiple of 22 and 26, which is 572:
572 * (d / 22) + 572 * (d / 26) = 572 * 0.9
This simplifies to:
26d + 22d = 514.8
Combine like terms:
48d = 514.8
Divide both sides by 48:
d = 10.725
So, the distance to her friend's house is approximately 10.725 km rounded to the nearest 0.1 km.