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# Bus A and Bus B leave the bus depot at 8 am. Bus A takes 25 minutes to complete its route once and bus B takes 35 minutes to complete its

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Bus A and Bus B leave the bus depot at 8 am.
Bus A takes 25 minutes to complete its route once and bus B takes 35 minutes to complete its route once.
If both buses continue to repeat their route, at what time will they be back at the bus depot together?
Assume the buses have no breaks in between routes.

Feb 24, 2021

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• Listen man, this is simple, when the speed is constant, like here, there is only one formula that describes movement ov various objects, vehicles, whatever, and it is
• V=S/t= const. (V[m/s] is speed, S[m] is distance covered at that speed in average, and t[s] is TIME.

TIME is the same for both busses, and by time i mean the time that "goes by", understand? It is not possible that 2 different objects experience different time from one moment to another, and this goes beyond and type of movement, or whatever they do or not do - time that passed is THE SAME for both!

Also, in the text should be more clearly noted that those 2 busses have the same lenght of single route to cover. This must be so, since there are to few data otherwise. Keeping theese 2 FACTS in mind, that forementioned time, which passed from 08.00h am up to the moment that the met again (they started at the same time) is actually the smallest number which can be divided with both of their times for one route. Those times are 25 min. for Bus A, and 35 min. for Bus B.

• There is a cousy method when you search this number, and it consists of (if numbers are not simple, meaning devidable with only 1 and themselfes, than you must multiply them, and if it is visible that those numbers can be divided with other numbers. Here it is 5 for 25, and 5 and 7 for 35. The minimal number which can be divided with both 25 and 35 is the smaller number from 2 results.
• We multiply one number (25) with divider of another (5, 7 and first we thry wih smaller, 5) and vice versa (35 we can multiply only with 5) ⇒ 25·7=175 and 5·35=175 so all is clear since if this is the case - that is the number!

• They shall meet after 175 minutes, or 5 minutes short of 3h, or after 2h and 55 minutes of driving with no stoping.

• # Time of their meting in depo will be: 1055 AM

P.S.

(One can add, that for that period, Bus A (faster one) shall make 7 rounds, and Bus B just 5. One more number that verifies that this is all correct is that both of numbers for routes are odd, and they must be, which means that the randevou point is the opposite depot from the starting one)

(Having one odd and one pair number for number of routes, will mean that calculation is wrong, which it aint, of course).

Very best regards,

Озрен Карталовић,

master of electrical sciences and computers (IT)

Contact details deleted - Melody.

Feb 24, 2021
edited by Ozren  Feb 24, 2021
edited by Melody  Feb 24, 2021