Hello,
This is a problem based on the relationship between Speed and Distance when time is constant. When time is constant, Speed varies directly with Distance. Now, let us look at a time saving approach while attempting such problems with variables.
Since the distance between Townville and Villageton is being expressed as a variable i.e. 2K kilometres, the best thing to do in such cases is to assume simple but workable values for K. In our case, a good value to assume could be 100. So, the distance between Townville and Villageton becomes 200 kilometres.
Secondly, the actual speeds of Ann and Bea have not been given, but a relationship between their speeds is given in terms of a ratio. Therefore, it makes sense to assume simple values for these variables as well. It’s specified that Ann’s speed is 4 times Bea’s speed. So, we can assume Bea’s speed as 10 km per hour and consequently, Ann’s speed will become 40 km per hour.
Since they start off together from Townville, Ann will reach Villageton in 5 hours (200km/40kmph). In these 5 hours, Bea would have traveled 50 km or in other words, he would be 50 km away from Townsville.
Attachment:
Ann and Bea leave Townville at the same time and travel - 1.JPG [ 18.27 KiB | Viewed 7604 times ]
At this point again, both of them start their respective journeys at the same time (albeit traveling towards each other). Hence, the total distance of 150 km between them will have to be divided in the ratio of their speeds, which is 4:1.
Therefore, distance travelled by Ann = (4/5) * 150 = 120 and
distance travelled by Bea = (1/5) * 150 = 30.
Attachment:
Ann and Bea leave Townville at the same time and travel - 2.JPG [ 22.6 KiB | Viewed 7563 times ]
Hence, Bea has travelled a total of 80 km by the time they meet. 80, when compared to the total distance of 200 is 40% or (2/5)th. But we have assumed 200 as 2K.
Hence, the total distance travelled by (2/5) * 2K = 4K/5. Hence, the answer option is E.
An interesting aspect of this question is that, the second part of the question (where 150 km is to be covered together by Ann and Bea) can also be solved by using Relative Speed concepts. However, it is not a necessity, and it has already been shown above that, without knowing the relative speed concepts also, you will be able to arrive at the answer with a fair degree of ease.
Hope this helps!
Cheers,
CrackVerbal Academics Team