A bee files at 20 feet per second directly to an orange groove from its hive. The bee stays at the orange groove for 15 min , then files directly back to the hive at 12 feet per second. It is away from the hive for a total of 20 mins.
a) What equation can you use to find the distance of the orange grove from the hive ?
b) How far is the orange grove from the hive ?

The correct answer is: bee hive is 2,250 feet away from the orange groove

Step-by-step solution:-
Let the distance between bee hive and the orange groove be x ft.
Total time taken = 20 min
Total time taken = 20 60 sec ....................................................... (1min = 60 sec)
Total time taken = 1,200 sec .......................................................... (Equation i)
Now, we know that-
Time = Distance/speed
∴ Time taken while going to the orange groove = Distance/ speed
∴ Time taken while going to the orange groove = x/20 sec ...................................... (Equation ii)
Waiting time at the orange groove = 15 min
Waiting time at the orange groove = 15 60 sec ............................................. (1min = 60 sec)
Waiting time at the orange groove = 900 sec .............................................................. (Equation iii)
Time taken while coming back to the hive = Distance/Speed
∴ Time taken while coming back to the hive = x/12 sec ........................................................ (Equation iv)
Total time taken = Time taken while going from hive to the groove + waiting time + Time taken while coming back to the hive
∴ 1,200 = x/20 + 75 + x/12 ......................................................................... (From Equations i, ii, iii & iv)
∴ 1,200 = x/20 + x/12 + 900
∴ 1,200 - 900 = (12x + 20x)/240 .......................................................................... (Taking all constants together & making the denominators equal on RHS)
∴ 300 = 32x/240
∴ 300 × 240/32 = x ............................................ (Multiplying both sides by 240/32)
i.e. x = 2,250 feet
Final Answer:-
∴ Equation that can be used to find the distance between bee hive and the orange groove is- 1,200 = x/20 + 75 + x/12.
Also, bee hive is 2,250 feet away from the orange groove.