A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. What is the speed of the train?

Question

Kennedy Adams · Accepted Answer

#40# km/h

Suppose the speed of the train is #x# km/h. It takes #480/x# hours to travel, but if the speed were 8 km/h slower, it would take #480/(x-8)# hours. Now we've got the equation: #480/(x-8)# = #480/x# +#3# This can be solved as follows. Don't forget that the answer must be positive, so the speed is #x=40# km/h. Let's see how much time it takes. Traveling at 40 km/h takes 12 hours, and traveling at 32 km/h takes 15 hours. The difference is three hours, and the answer is correct.

Genesis Allen · Answer

#40 (km)/h# Total Distance #S=480 km# Formula For Speed #"speed"="distance"/"time"# Hence #"distance"="speed"xx"time"# Case-I let the uniform speed of Train #=v (km)/h# and the time taken to complete distance #=(t ) "hour"# Distance #S="speed"xx"time"=vt# . . . . . (equation 1) Case-II If speed has been 8km/h less then train would have taken 3 hours more to cover the same distance. Now in this situation speed of train #=(v-8) (km)/h# and Time taken to complete distance #=(t+3) hour# Distance #S="speed"xx"time"=(v-8)(t+3)# . . . . . (equation 2) Since Distance for both cases are same . Comparing equation 1 and equation 2, we get #=>vt=(v-8)(t+3)# #=>vt=(v)(t+3)-8(t+3)=vt+3v-8t-24# cancel vt from both side #=>0=3v-8t-24# #=>3v-8t=24# #=>3v=24+8t# #=>v=(24+8t)/3# but from equation 1 the value of #t=S/v=480/v (hour)# #=>3v=24+8(480/v)# #=>3v^2=24v+3840# #=>3v^2-24v-3840=0# #=>v^2-8v-1280=0# factorize the quadratic equation #=>(v-40)(v+32)=0# #v# is either #40 (km)/h# or #-32 (km)/h# Speed is Positive hence #"Speed"=40 (km)/h#

Avery Alexander · Answer

undefined The speed of the train is 80 km/h.