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A bird leaves its nest and travels 12 miles per hour downwind for x hours. On the return trip, the bird travels 2 miles per hour slower and has 3 miles left after x hours.

What's the distance of the entire trip?

How long does the entire trip take?

Verified Answer :

12x = 10x + 3

Subtract 10x from both sides

2x = 3
Divide by two on each side

x = 3/2 or 1 1/2 hours



Distance of the trip:

12 2 3/2 = 36 miles

How long does the trip take:

3/2 + 3/2 + 3/10 = 3 3/10 hours

Answer:

a) 36 miles

b) 3.3 hours

Step-by-step explanation:

Given:

Downwind speed of the bird = 12 mph

Time for travel = x hours

Speed at the return = 12 mph - 2 mph = 10 mph

Distance left = 3 miles

Now,

The distance covered at 12 mph = 12 × x = 12x

now,

distance covered with speed 10 mph in x hours = 10x

also,

10x + 3 = 12x

or

2x = 3

or

x = 1.5 hours

Therefore,

the distance of the entire trip = 2 × 12x = 2 × 12 × 1.5 = 36 miles

Now,

the time taken to complete remaining 3 miles while returning = \(\frac{3}{10}\)=0.3 hours

hence,

the total time for the entire trip = 2 × 1.5 + 0.3 = 3.3 hours